The Toffees would have moved joint level with Manchester United in second had they beaten Newcastle on Monday night but they were denied by a last-minute Demba Ba equaliser.
Moyes said: "We've quite often done that and not got in the position we really want to be, 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."
It was a night where Everton showed solidarity with their city rivals Liverpool as they remembered the victims of the Hillsborough disaster and their families' long fight for justice.
But all the talking points at the end of the match were about the performances of the officials after Marouane Fellaini was denied a goal by an errant offside flag before Victor Anichebe's header clearly crossed the line but was also not given.
Goal-line technology has already been approved by FIFA and Moyes accepts it is only a matter of time before it is introduced in the Premier League, but his main disappointment was that his team could not hold onto their lead.
He said: "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.
"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. We've been pleased with our form, with the performances of the players.
"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."
Swansea have also had a good start to the season under new manager Michael Laudrup and sit level on seven points with Everton but two places ahead in fifth because of their superior goal difference.
The Toffees won both of their Premier League meetings last season, keeping clean sheets both times, but Moyes believes Swansea pose a greater goal threat under Laudrup than they did under predecessor Brendan Rodgers.
He said: "Swansea are a really good side and have done great but it's a different season, a new manager.
"From what I've seen already I think he's slightly different to Brendan in how they play, I don't think you're going to see an identical Swansea to last year.
"They look as if they can score goals, they've got a little bit more threat and they've shown that."
Everton will definitely be without striker Nikica Jelavic for the trip. The Croatian bruised his knee and shin in a collision with a post early on against Newcastle and, although he tried to carry on, he was substituted later in the first half.
Midfielder Darron Gibson is also out as he continues his recovery from a thigh strain while full-back Tony Hibbert is a doubt after picking up a knock.