The midfielder signed for the Toffees from Manchester United on Friday for £2.5m.
"I thought Gibson played well, he put a great ball through for Tim Cahill and I thought he should have possibly connected to it," Moyes told reporters.
"He'll benefit from some regular games, you can see he just ran out of steam midway through the second half.
"Anyone who saw the game would think he did a decent job for us. I think nine or 10 Premier League clubs would like to have signed Darron Gibson."
The point has moved Everton up to 10th in the Premier League table.