The sides clash again on Sunday in an FA Cup fifth round clash at Goodison Park, with Everton out to gain a measure of revenge for that loss.
Since then Everton have lost just one of 12 games and given themselves an outside chance of even claiming a Champions League spot.
Moyes said: "We will keep going for a Champions League place, at the moment we have a lot of points to catch up.
"But it looks like Aston Villa will be the team to break into the top four this season, if that is going to happen.
"We aim to continue our good run and hope that teams above us drop points. If we keep this form going until the end of the season, who knows?
"Since Villa won at Goodison Park they have been in fantastic form and I have always said they look the best bet of sides trying to break into the Champions League.
"But if we had started our season better we would have been up there to. But if we keep our current form going, we will be up there at the end with Villa."
Moyes added: "We were all disappointed with the way we lost to them here, when we felt we had done enough to get a draw.
"But they showed that they don't give in, when we equalised it didn't get to them. But we have learned from that too, we have been in a good run and tidied ourselves up from that point.
"That result could have sent us under, it was such a disappointment and we could have found it difficult to pick ourselves up.
"But it has been the exact opposite. We have picked ourselves up and got on with things. We have gone from strength to strength.
"We recovered from that because of the character we have amongst the players at Everton.
"Maybe others would have said they were unlucky and it wasn't going to be their year. But we have dug in, rolled our sleeves up and got better results.
"Everyone that day went away numb, to lose 3-2 in the last seconds was hard to take. But look how we have bounced back since."
Moyes has great respect for Villa and the way they have forced their way into the top four.
He added: "Villa have great pace, they are a great counter-attacking side and deliver a lot of crosses into the box. They have an attacking edge with the players they have.
"They now have Emile Heskey and John Carew and they are a very well balanced side and could finish in a Champions League spot.
"But our lads have been playing really well, they are resilient, they are in outstanding form.
"I am trying to keep that side together as much as possible. But injuries and suspension are kicking in and we know we have problems because we are short on numbers."
Everton will be without the cup-tied Jo, on loan from Manchester City, while record signing Marouane Fellaini is also out with a damaged back, a small crack in a bone now expected to keep him out for three weeks.
The club are hoping that striker Louis Saha, out since November with a hamstring problem, will be able to return on the bench. Steven Pienaar, out for a fortnight with a similar injury, is also serving a ban following five bookings.
Moyes confirmed that Victor Anichebe, the young striker he fell out with after a training ground row recently, is fit, but would not discuss whether the youngster is in line for a recall.
, Draw 2/1
, Aston Villa 12/5