Steve Round was disappointed Everton were not able to defeat Sunderland at the first attempt after a 1-1 draw at Goodison Park in their FA Cup quarter-final.
Sunderland were second best for much of the match and goalkeeper Simon Mignolet kept the Black Cats in it late on with a fantastic double save, stopping a header from John Heitinga at full stretch before recovering to deny Nikica Jealvic with the rebound.
And the Toffees assistant manager felt that their second-half performance in particular meant they should have taken the win.
"We thought we did everything we could in the second half except stick the ball in the net," he said.
"We piled on the pressure and had opportunity after opportunity, culminating in that double save, which was tremendous from their perspective.
"The lads are disappointed in there that we couldn't turn pressure into a goal.
"It took us a while to get a foothold but the last 20 minutes of the first half and all the second half, I thought we were terrific and unfortunate not to win."
Everton's players felt they should have had at least one penalty in the game, arguing that Royston Drenthe was upended in the box by Craig Gardner and John O'Shea handled the ball.
Despite referee Andre Marriner only being a couple of yards away from Gardner's challenge in the 16th minute, he saw nothing untoward, but Round was convinced it was a penalty.
He added: "It was a clear foul. Maybe it was too early for the referee but he was right there on the spot and we don't know why he didn't give it.
"I thought Roy (Drenthe) didn't get much of the rub of the green. I thought he was fouled on numerous occasions.
"Whether they think he is diving or not - obviously he isn't because he is getting fouled.
"He is so small, he hits the deck. We are a little disappointed he didn't get more fouls than we expected."
The Everton assistant manager felt the second decision was not as straightforward.
He said: "That is a bit of an interpretation. We think it would be, they wouldn't, but the referee made a call and we have to accept that."