Andy Carroll's goal three minutes from time saw Liverpool progress to the final after the Toffees had gone ahead in the first half through Nikica Jelavic.
The FA Cup represents the closest Everton have come to winning a trophy in Moyes' nearly 11 years in charge at Goodison Park, having lost out to Chelsea in 2009 despite Louis Saha's fastest-ever goal in a cup final.
But even with his side well placed to put the pressure on for a place in next season's UEFA Champions League, Moyes is striving to win some silverware, with Wigan his side's quarter-final opponents.
"I still have the disappointment of the semi-final against Liverpool and nothing would give me more pleasure than to get Everton back to Wembley, to try to reach another final," said Moyes.
"I know the players are very much of the same feeling and, although FA Cup ties are never easy, we will be striving to put right the disappointment from last year."
Goalkeeper Tim Howard has mirrored his manager's determination to bring the FA Cup back to Goodison Park for the first time since 1995.
"What happened to us last year has given us a real drive to get back there again," Howard admitted. "It is always tough to lose to Liverpool - and even more so in those circumstances and on that big occasion."