"I want to wait, but my feeling is not good for both," Mourinho told reporters after his side's 2-1 extra-time win at Old Trafford on Thursday completed a 3-2 aggregate victory.
"I want to wait and I want to try to be optimistic, but I'm not."
Centre-back Rojo was stretchered off with a leg injury in the first half, while Ibrahimovic, United's 28-goal top scorer, hobbled off in stoppage time after his right knee bent the wrong way.
Mourinho said he expected to find out more about the two players' injuries within "a couple of days".
Marcus Rashford proved a capable deputy for Ibrahimovic, netting a smartly taken winner to send United into the competition semi-finals for the first time.
The 19-year-old had also scored the opening goal in United's 2-0 win over Chelsea on Sunday after Ibrahimovic was rested.
Daley Blind took over from Rojo, but Mourinho has fewer options in central defence, with Chris Smalling and Phil Jones both currently sidelined.
The pair sustained injuries on England duty a month ago, Smalling injuring his knee and Jones his foot.
Mourinho said both players would be able to come back sooner than anticipated if they put their minds to it.
"I think it's time for Jones and Smalling to be brave, to risk," said the Portuguese, whose side visit Burnley in the Premier League on Sunday before tackling Manchester City next Thursday.
"Because for the team, you have to do everything. That's the way I think. You cannot do miracles. I don't expect miracles. But you have to try to do everything to accelerate the process.
"Even with a crazy mentality, they cannot play Sunday. There are no miracles.
"But with a special spirit, you can (play) sooner than expected. So instead of come mid-May, you can come beginning of May."
Asked when the pair were likely to be back in action, Mourinho replied: "If it was me, I think tomorrow."
Mourinho had kinder words for left-back Luke Shaw, having publicly and sharply criticised the England international on several occasions in recent weeks.
"Luke Shaw did something new for me with him that means a lot for me," he said.
"After 90 minutes, before I know that I have to change Zlatan, he was with cramps. I had Ashley Young ready to come on and he told me, 'I am going to play these 30 minutes with cramps. No problem.
"'If you need to make a change in another position, do it, because I'm ready for it.'
"These are the kind of things that make me trust a player. Mentality is fundamental."
Mourinho also expressed reservations about reports England Under-21 coach Aidy Boothroyd plans to call Rashford up for this year's Under-21 European Championship in Poland.
"He cannot play every game," Mourinho said after being asked if Rashford was capable of filling in for Ibrahimovic.
"On top of that, I think you are trying to take him for the Euro Under-21s. It's hard for the kid in terms of playing every match, but I always trust the players with a special mentality."
Rashford teed up Henrikh Mkhitaryan for a 10th-minute goal that put United 2-1 up on aggregate, only for captain Sofiane Hanni to equalise for Anderlecht in the 32nd minute.
Roared on by their raucous away support, Anderlecht gave United several scares before finally succumbing in the 107th minute.
"We played a very good match. Unfortunately the result isn't so good," said the Belgians' coach Rene Weiler.
"We played very well in the first half. We equalised, but couldn't score a second goal. When you concede a winner in extra time, it's always difficult to find a way back."