The midfielder has missed around four months of the ongoing Premier League season with a persistent thigh injury.
However, despite the fact that he has returned to the team in recent weeks, Moyes has admitted that the Irishman has still not recovered fully from the problem.
"After the game on Saturday, I was asked about Darron Gibson's goal and his shot. I think he could do it more and with more ferocity as well because he's got a great shot on him," said the Scot.
"He has got a bit of a problem at the top of his thigh which will probably require an operation at the end of the season."
Gibson joined the Toffees from Manchester United in January 2012.