Assistant manager Steve Round admitted his frustration at the 1-1 draw with Sunderland - but insists the Blues can still progress to the FA Cup semi-finals.
Tim Cahill's 23rd-minute header levelled Saturday's quarter-final at Goodison Park following Phil Bardsley's earlier opener.
With neither side able to find a winner, Everton now face a tricky replay at the Stadium of Light, but David Moyes' No. 2 remains hopeful of a place in the final four.
Round said: "We're very disappointed not to have gone on and won the game in the second half. We had enough dominance of possession and enough opportunities.
"Balls were flashing in and around the box and their goalkeeper [Simon Mignolet] has made a wonderful double save at the end.
"It's an opportunity missed," he continued. "They'll start as favourites at home obviously. But Everton have a knack of upsetting those odds at times. Last season we drew at home against Chelsea and then went away and won.
"So it's within our capabilities, that's for sure."
Cahill turned in a Man of the Match performance on his return to the starting line-up and Round added: "I thought Tim was terrific today. He looked fresh and full of energy. He was a threat in both boxes and he linked us up really well. He deserved his goal."
Round also felt the hosts were perhaps unfortunate not to get more from referee Andre Marriner.
"On another day, maybe we would get a penalty or two," he said. "Personally, I think there was one penalty for definite on [Royston] Drenthe in the first few minutes. The second one was a handball. We think it's a penalty, they would say it's not a penalty.
"It's an interpretation by the referee at that time as to whether he's handled it or the ball has hit his arm and he couldn't do anything about it. It's one of those decisions that you either get or you don't.
"That's the referee's interpretation. There's not much I can argue with that really - it's his call."