Manchester United eventually won 2-1 in extra-time to advance to the semi-finals with a 3-2 aggregate victory.
It should have been plain sailing for Jose Mourinho's men after Henrikh Mkhitaryan had given them the lead early on, only for Sofiane Hanni to equalise before half-time.
The Armenian, reintroduced to the starting XI after being rested over the weekend, claimed his fifth goal in Europe this season after 10 minutes, powering home into the bottom corner from Marcus Rashford's lay-off.
Rojo was carried off in the first half on a stretcher while Ibrahimovic hobbled off late in the game after landing awkwardly following an aerial challenge.
"So when you reach a certain level - and he has reached that level - then I don't think it makes sense".
Mourinho:"I want to wait but my feeling is not good, for both".
"But the news is fairly negative I think".
INJURY: Neuer to miss the rest of the season
Winger Arjen Robben said, "it's such a shame that such a super game, such a top game, is decided by one man with a whistle". This confirmation of Real Madrid's interest will surely have consecuences. "He knocked us out".
But faced with a growing injury list, Mourinho said he doesn't want to see Rashford playing at age-group level.
"OK, you speak about his qualities, his quality is fantastic", Mourinho told reporters at Old Trafford.
With both men now sidelined, he said: "I think it's time".
And it was an advantage they didn't relinquish to book their place in the last four, and they will find out who they play in the semi-finals when the draw is made later on this morning.
"There are no miracles, but with a special spirit you can sooner than expected. So instead of mid-May, it could be the beginning of May, this kind of acceleration of the process".
United were unconvincing and missed scores of chances against the Belgians, leaving Mourinho looking exhausted and sounding tetchy during his press conference.
"I imagine the players are more exhausted then me but we are in the draw tomorrow and we still have the dream to win the competition".
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