The Toffees manager is still feeling the "disappointment" of last year's exit, while the keeper believes that the club are not performing to the best of their abilities just yet
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And the boss insisted that he would love nothing more than to lead his team to Wembley once more, something that might fill the void left by the exit to the Reds.
The Scot told reporters: "I still have the disappointment of the FA Cup semi-final last year against Liverpool and nothing would give me more pleasure than to get Everton back to Wembley to try and reach another final."
Moyes' men have been drawn at home against fellow Premier League side Wigan in the quarter-finals of this year's competition.
Goalkeeper Howard believes the draw gives them a good chance of progression, also admitting they are riding on the disappointment of their last campaign.
He added: "What happened to us last year has given us a real drive to get back there, but the way Wembley makes me feel, makes the team feel and makes the fans feel, is also giving us that drive.
"It's always tough to lose to Liverpool, more so in those circumstances and on that big occasion.
"In order for us to experience that again, we have to get past Wigan. But the draw has been favourable and it was good to get a home draw finally."
The USA international also thinks the Goodison outfit are yet to reach their peak this season, while indicating their small squad means they may rely heavily of their "big players".
"I don't think we are firing on all cylinders and, at the moment, I think that's a good thing," the 33-year-old continued.
"Let's hope we have something in reserve. We spent a lot of energy in the first half of the season and now it's more about our big players.
"We don't have a large squad so it's going to be about the big players producing. Most of the teams around us can chop and change their team on a given weekend and still have a lot of firepower."