Gill followed Sir Alex Ferguson out the exit door to be replaced by Ed Woodward.
Dalglish told talkSPORT: "I think also what was a big thing, which doesn't get much publicity, was David Gill moving on and Ed Woodward coming in. That has had an impact on Manchester United as well.
"Maybe they should have asked David Gill to stay on during the transfer window to give his advice and his knowledge to both Woodward and Moyes. I think it would have been helpful to both of them.
"Moyes will be OK. There is no problem there. It's not as if he's being threatened with the sack. There is disappointment about their results but their standards have been set so high anybody would have disappointed."