The visitors started poorly and fell behind when Emmanuel Dennis lobbed Sergio Romero early in the first half.
United equalised when Anthony Martial raced through to beat ex-Liverpool keeper Simon Mignolet one-on-one.
“I don’t think it was one of the best games anyone’s seen,” Solskjaer said.
“It was a difficult game against a well-organised team in difficult conditions.
“We got an away goal, we got a draw. We go home next week so hopefully we can finish the job.”
The game was played in heavy rain and strong wind for large periods, while Solskjaer also felt the ball that is used in Europa League games did not help improve the quality of football on display.
“I think you can ask any of the players, that ball doesn’t help anyone play football,” he added.
“It’s just different and difficult to play with. You can get one and try!
“But it’s the same for the two teams, of course. But the conditions weren’t nice, the wind and the rain.”
The two sides will meet again at Old Trafford on 27 February.
Martial puts below-par United in driving seat
After back-to-back Premier League defeats in January, Manchester United have enjoyed an upturn in form in recent weeks with three wins and a draw in their four games before the trip to Belgium.
An impressive 2-0 win at Chelsea on Monday gave United the ideal platform to build on but six changes to that side threatened to disrupt any momentum they were building and so it proved as the visitors put in a disjointed and uninspiring performance for large periods of this game.
United’s three-man defence – particularly in the opening half hour – looked fragile and exposed and Ole Gunnar Solskjaer’s side failed to heed an early warning when Nigerian striker Dennis got in on the right before Victor Lindelof scrambled away.
Consequently, they were punished after 15 minutes when Mignolet launched a pass down the pitch and Dennis got in between two defenders before coolly lifting the ball over the onrushing Romero.
From then on Bruges looked certain to add to their lead as United struggled to settle but a mistake at the back was clinically pounced on by Martial as he ran on to a poor throw-in, outpaced a defender before beating Mignolet at his near post.
Martial has often struggled to live up to the high expectations placed upon him when United paid £36m to sign the forward from Monaco in 2015, making him the most expensive teenager in world football.
However, he was the standout United player in this game and was unlucky not to add a second when Mignolet pushed his shot onto the post just before half-time.
Martial has now scored in back-to-back games and, with 14 goals to his name already, he is on course to surpass his previous best tally for a season – the 17 he scored in his debut campaign for United in 2015-16.
Another positive to come from the game was the late cameo from Bruno Fernandes. The Portugal midfielder – signed from Sporting Lisbon in January – was introduced with nine minutes to go but his desire to get the ball and his positive, forward thinking was yet another indication that he can become a key player for United in the coming seasons.
Dennis shines for bold Bruges
Emmanuel Dennis misses a chance against Manchester United
Dennis was linked with a move to the Premier League in January
Club Bruges went into this game as a side in form. The Belgians are the runaway leaders in their domestic league and were unbeaten in their 12 previous games in all competitions.
The confidence such a good run provides was evident from the outset as they took the game to United, led by the hugely impressive Dennis.
The Nigeria international has shown he is a player for the big occasions, having scored two goals against Real Madrid in the Champions League this season – before Bruges dropped into the Europa League – and he was unfortunate not to finish with a couple of goals on Thursday.
His quick feet and good close control was a constant menace to the visiting defence and he will be the player Solskjaer’s side will need to be the most wary of if they are to avoid an upset in the return leg.
Man of the match – Anthony Martial
Anthony Martial scores against Club Bruges
Martial worked hard in a first half in which his team-mates struggled to have an impact and his goal could prove crucial
‘Right to make changes’ – what they said
Philippe Clement, Club Bruges coach: “At this moment I am not concerned whether we could qualify or not next week. We still have three games coming up in nine days.
“At least I want my players to show courage and guts in Manchester. It’s important for the guys to have that experience and then we will see. We still need the same luck there as for the game today.”
Manchester United boss Ole Gunnar Solskjaer, speaking to BT Sport: “It was a game with difficult conditions. We gave them a goal on their goal kick and they gave us a goal from a throw in so it was two poor goals in concentration from both teams.
“There were some moments from us where we switched off. We were not really at the races to start with but a draw, we got the away goal so we are looking forward to next week.”
Right to make so many changes? “We needed to keep using the squad, we need to use the players and give them the chance to play their way into the team and into form because there are so many games. Tonight was worth making those changes. We have a big game on Sunday against Watford.”
Mignolet makes it count – the stats
Manchester United are unbeaten in their last four away games in all competitions (W3 D1), their longest unbeaten streak on the road since March 2019, when they won nine in a row.
Club Bruges have kept just one clean sheet in their last 10 Europa League matches, failing to do so in their last five games in the competition (excluding qualifiers).
Dennis’ opener against United ended the English side’s run of 408 minutes without conceding in all competitions.
United forward Martial has been directly involved in four goals in his last four appearances on the road in all competitions (three goals, one assist), as many as in his previous 10 games.
Mignolet is the first goalkeeper to provide an assist in the Europa League since Guilherme for Lokomotiv Moscow against Sporting Lisbon in September 2015.
Manchester United return to Premier League action this weekend as they host Watford on Sunday, 23 February (14:00 GMT).