Landon Donovan issued an apology to his team-mates in the White Hart Lane dressing room after missing an open goal against Tottenham on Sunday.
The United States forward, who came on as a substitute, admits he cannot understand how he stabbed his finish wide after being picked out by Jack Rodwell at the far post.
"Landon said sorry to us afterwards," said midfielder Mikel Arteta.
Donovan came on to chase the game and earn Everton a draw to help their bid for a European place as they recover from a poor start to the season.
"This is just a really disappointing moment for me personally," Donovan, 27, said. "I've put a lot into my time here and another goal would have been a nice reward.
"I got myself in a good position at the back post and was hoping Jack was going to put the ball across goal. He did that and it came perfectly for me.
"It's hard to understand what went wrong. I felt like everything was right but then I looked up to see the ball had hit the side-netting.
"It's so frustrating because if we had scored then it's possible we might have gone on to win the game.
"It's tough but we've got to put this behind us now and move on. There are still a lot of points to play for."
Everton boss David Moyes admits it is a long shot for his side to join the race for the top four - "we would need to be on an incredible run" is his assessment - but has been encouraged by Phil Jagielka's return to the squad following his recovery from a serious knee injury.
"He made a massive difference when he came on against Spurs," Moyes said. "On his day he's a really top defender. He's probably not ready for 90 minutes yet."
Moyes, when asked about Jagielka's England chances, added: "He was certainly in their views. If he plays like he did against Spurs he's not far away."
Louis Saha missed the trip to Spurs with injuries to his hamstring and Achilles, problems that led to France calling up former Liverpool striker Djibril Cisse for the friendly against Spain on Wednesday.
