Moyes has yet to win a trophy in nearly 11 years at the club and the FA Cup, which the Toffees last lifted in 1995, remains one of his most sought-after targets even if he believes it has lost some of its appeal for other clubs.
"We want to go as far as we can in the FA Cup," he added.
"We'll not under-estimate Cheltenham and we'll have to go there and do a really good job if we are to get through to the next round.
"It is something where Everton have had success at times and it is a trophy people would like you to be involved in.
"We've been to one final, got to the semi-final last season so we'd like to do it again and get to the cup final.
"I think it has lost its excitement a little bit, as it goes on it gets better.
"There is so much at stake now in the Premier League, there is so much coverage, so in a way the FA Cup has been put on the back burner.
"But I think it is a cup competition every team wants to win but if you really pushed the chairmen and managers of clubs they would say certainly doing well in the Premier League is the priority."