United had a number of chances to put the game out of Anderlecht's reach after Henrikh Mkhitaryan's opener, but they failed to score a second goal and were eventually made to pay when Leander Dendoncker drew things level late on Thursday.
Mourinho took aim at his attackers after the final whistle and Ibrahimovic has now acknowledged they should indeed have done better.
"I think he is right in this matter because I was not feeling good in the sense of I was feeling tired," the former Sweden international stated.
"But it is not an excuse because I still have to do well, I still have to do much more and much better than I did. I speak for myself and [Anderlecht] was not a good performance.
"We have one month to go, it is many games we play. I have been playing almost all the games.
"But we are still grinding, we are still pushing because we have the Europa League and the end of the Premier League. We fight for it."
Ibrahimovic will be looking to get back to his best when United take on Premier League leaders Chelsea on Sunday, but he realises they are in for a tough task.
"I think they are a good team. Overall a good team and then of course they are playing once a week which makes a difference also because at the end of the season, I do not know how many games we have in total but I think we have much more than them," he added.
"They have not been playing in Europe this season and they went out from the League Cup early. But they have a great team, or else they would not be number one.
"I think our unbeaten league run is nothing we focus on. I would prefer to be first in the league and not having this record. It does not give us anything, this record."