Both players had to be taken off in the Manchester derby defeat and the Chilean confirmed it will take time for them to recover, meaning they will not be available for international duty.
Speaking in his post-match press conference, he explained: "Both of them have muscle injuries - Raheem in his groin; Joe in his calf.
"I don’t think muscle injuries can heal in one week. They normally need three or four weeks."
The defeat cut the gap between the Blues and their neighbours to a single point but Pellegrini asserted his side are not looking over their shoulders - only upwards.
"We continue in fourth position," he added. "We have to play for another 24 points. We must be focused on the next game.
I am not unhappy with the performance of the team. We had 26 attempts on their goal and we dominated the game but missed chances to score.
The Blues boss also dismissed the suggestion the players are lacking in confidence or concentration.
"It is not the best way to finish the season," he conceded, "but I am happy with the players’ attitude. They are all focused and they want to finish as near to the top as possible.
"We have another 24 points to play for and every game is different. United did not play better than us.
"It was a mistake in the lead up to the first goal. I don’t remember a lot of chances United had - they had just one after the goal."