With little time to recover from Monday's Premier League victory at Chelsea, the Reds crossed the Channel to take on the Belgian leaders on a blustery night in Bruges.
Emmanuel Dennis got Club Brugge off to a dream start after catching the normally-dependable Sergio Romero well out of position, but Anthony Martial capitalised on an error to silence the tired Jan Breydelstadion and seal a 1-1 draw.
That away goal means United have the upper hand heading back to Old Trafford for the second leg of this last-32 tie, leaving Solskjaer pleased on the whole.
"It was a difficult game against a well-organised team in difficult conditions," he said. "I don't think it was one of the best games that anyone's seen. A bit sloppy concentration-wise, but the conditions with the pitch and the ball makes it hard.
"I think you can ask any of the players. That ball doesn't help anyone play football. We needed to make everyone part of the squad (so I made changes), gave them games.
"We've got so many games now, so we got an away goal, we got a draw. We go home next week so hopefully we can finish the job."
Having taken the upper hand in their Europa League tie, it's back to Premier League action on Sunday for United as they welcome Nigel Pearson's Watford to Old Trafford.
The Red Devils currently find themselves in seventh place in the table, while the Hornets are battling for their Premier League survival down in 19th spot in the standings.
United will be looking for some revenge this weekend after they suffered a 2-0 defeat at the hands of Watford back in December.