The Scot insists securing a place in Europe is the next step for his side and admits he was disappointed with the 2-2 draw against Newcastle United on Monday
Moyes' side have secured seven points from their opening four Premier League games and were denied a victory in their last outing against Newcastle United on Monday following Demba Ba's late equaliser.
"We've quite often done that and not got in the position we really want to be,” Moyes told reporters. “Whether that's cup finals or semi-finals or the chance to push ourselves into a really strong league position, so it's the next step we have to try to take."
Marouane Fellaini was denied a goal after being wrongly judged offside in Everton's 2-2 draw with Newcastle United, while Victor Anichebe’s header, which crossed the line, was ruled out by officials.
"The goal-line one you can say needs technology but the offside one is not going to change, so that disappointed me as much as the goal-line one,” Moyes added.
"Technology will come in on the goal-line, I've got no doubt about that, and I think it's moving forward.
"It's frustrating because it's their [the officials'] job to get it right and they didn't get it right but looking back at the DVD of how we played throughout the night was very good."
Swansea City have also recorded seven points from their opening four Premier League games this season but suffered their first defeat under new manager Michael Laudrup last weekend following a 2-0 loss at Aston Villa.
Moyes, meanwhile, has been buoyed by Everton's early displays but admits he was disappointed with the result against Alan Pardew's men on Monday.
“We've been pleased with our form, with the performances of the players," said Moyes.
"We could have won it and there's no-one else to blame but ourselves because we were 2-1 up with a few minutes to go and we didn't see it out. We have to play the games for 90 minutes and win them ourselves."