Louis Saha put the Toffees ahead before a late goal from Salomon Kalou earned Chelsea a draw and ensured the tie will go to a replay.
Moyes said: "I don't think you can come away and say Chelsea were really threatening. I thought we looked the side who were more likely to score than Chelsea.
"Petr Cech made some really good saves and that is what goalkeepers do.
"They had one shot which hit the outside of the post late on but overall I thought the players played really well.
"They performed well against a team that has not lost an FA Cup tie since 2008 and are Premier League champions. I have to give the players a lot of credit."
Source: PA
Source: PA