The Toffees boss will not prioritise one competition over the other as he believes his side can do well in both – and says not playing midweek European competitions is a bonus
The Toffees are in the race for fourth place in the Premier League, currently sitting in sixth place, seven points off Chelsea who are occupying the last Champions League spot.
Moyes' side are also in the quarter-finals of the FA Cup and will be looking to progress to the semi-finals with a home tie against Wigan to come next weekend.
The Scot suggests that he will play his strongest team for every game, regardless of which competition Everton are in, and claims his side are still in with a chance of gaining a Champions League place for next season.
"I hope we can do well in both," Moyes told reporters.
"I don't think you can ever prioritise one over the other. If we did, we'd be resting players in the Premier League for the cup.
"I see other managers do that, and I've done it myself, and you get criticised for it.
"I think all you can ever do is take one game at a time and move on.
"I still think we've an outside chance of finishing in a European spot, whether that be the Europa League or Champions League. While we've got that, we’ll have to keep driving on in the league games."
Moyes believes that although he has concerns over the size of his squad, one of the things Everton have going for them is that they are not playing in Europe and therefore do not have to worry about the strain of playing midweek games places on teams.
"We don't have European games. We've not got a barrel-load of midweek fixtures so I see no reason why we shouldn't treat every game on its merits," he continued.
"Of course, we have to worry about the size of our squad, but I can’t really change that."