Anderson has been battling to recover from a hamstring injury, whilst Pogba suffered an ankle problem in a reserve game earlier this week.
"Anderson is not going to play again this season and Paul got injured in Monday and he is out for the season," Sir Alex Ferguson said.
However, Ferguson has confirmed veteran striker Michael Owen has returned to training and could play some part, if not against Everton at Old Trafford on Sunday then at least in the following games against Manchester City, Swansea and Sunderland.
"I have said time and time again that Michael is a player who can score important goals if you are struggling in a match," Ferguson said.
"He has had a hard time with injuries. When he gets them it is usually months."
Ferguson also confirmed Ashley Young should shake off a minor knock to feature against Everton.