Chris Smalling and Nick Powell have both undergone operations but are expected to return for pre-season training with Manchester United.
Reds defender Smalling was on crutches during the lifting of the Barclays Premier League trophy after the win against Swansea while Powell has been missing from action at both senior and Under-21 level, despite Warren Joyce's side progressing to Monday's league final against Tottenham at Old Trafford.
"They are not long-term injuries," Sir Alex informed MUTV. "They will be ready for pre-season and that's the important thing. It's why we do these things.
"Chris had problems with his foot and had an operation on it. It'll be resolved and he'll be back for pre-season.
"Young Nick had a small operation to relieve a problem he had and he'll also be available for pre-season training. I knew I was not going to use them for the last part of the season, having won the league, so I think it was important to get the operations done."