Moyes’ men were within 15 minutes of going through to the fifth round before Chelsea substitute Salomon Kalou scored the equaliser to seal a replay at Stamford Bridge.
Everton had a chance to win the game just before Chelsea scored but Michael Essien produced a exceptional block to prevent a second goal for Everton.
Moyes believes that Everton were more than worth the win in today’s game given their second half performance.
“When you get in that position you want to finish the game off. We played well enough especially in the second half and I think the turning point was probably the Seamus Coleman header at the back post and then the last ditch tackle [from Essien],” he told ESPN.
“I thought the boys played well today, I can’t fault them. I can’t go in there and tell them they’ve done badly.
“You couldn’t come away from today and say Everton don’t deserve to be in the hat [for the fifth round draw] but obviously all we could get was a draw.
“We had a chance to make it 2-0 which didn’t quite go our way. If we had got that then I think we would have won.”
Everton appeared to play the better of the two teams in the second half and Moyes admits that Chelsea’s goal was unexpected when it came.
“It was against the run of play at that time, we had a bigger majority of control in the second half," he said of the goal.
“I thought we looked the more likely to score another goal.
“I don’t even know if [Nicolas] Anelka’s pass was meant for [Salomon] Kalou, I think it was meant for Ramires bursting through the middle and it was slightly behind him but if you take your chances and you’re willing to go forward then sometimes you score from it.
“They’re a good side and their play was good, they were well organised but we limited Chelsea to very few chances and I didn’t think we would concede a goal. I thought we were strong enough today to stop them."
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