The Red Devils made hard work of their last-eight tie against Danish side FC Copenhagen, giving up big chances at one end and missing a host of their own opportunities to score at the other.
In the end, Bruno Fernandes scored an extra-time penalty to settle the tie, after both he and Mason Greenwood had hit the post for United.
But Solskjaer says he was confident throughout that United would find a way through and needed to simply bide their time and wait for quality to play a telling part.
“It’s the third time this season, we’ve been to the semis in every competition we’ve been in,” he told BT Sport at full time.
“We deserved to win tonight, their ‘keeper was unbelievable but we hit the post, VAR decisions went against us and it could have been one of those nights where you end up with a [penalty] shoot-out.
“Sergio [Romero] didn’t have to make one save but we had to block and defend well, they made it hard for us. They had a game plan, triggers when they pressed us, a decent chance in the first half when they caught Fred on the ball.
“It was about being patient, not making mistakes and we knew we’d get chances. The [front four] will always create chances.
“I think we needed [extra time]. You don’t go gung-ho and leave them open for the counter-attack [late in games]; with another half an hour we’d create more chances and score.”
Solskjaer’s side will face Wolves or Sevilla in the last four, but the United boss wasn’t drawn on preferring a domestic rival, noting he ”had a last-16 [game] with Molde against Sevilla so I’ve got something to get back at them too.”