The Merseysiders sit sixth on the table four points behind the third-placed Gunners and two in arrears of fourth-placed Chelsea and fifth-placed Tottenham.
The fact that Everton have played more matches that both the Blues and Spurs, Moyes suggests that they will need to produce a perfect finish to the season by winning all five matches to be any chance of a champions League spot.
"We probably need to win all our games to have any chance but the players are playing well, we've had a couple of really hard away games and we keep picking up points," he told Sky Sports.
"I thought it was a really good game, it was end to end, we played some good stuff and we had to defend well.
"It was never going to be easy for us but I'm not going to be too despondent with a point even though I wanted to win it.
"We got a little bit fortunate and there were a couple of bits of fantastic defending to make sure we didn't concede a goal.
"We didn't have as many chances as we would have liked in the second half, but any manager who comes here knows that you're not going to get loads of opportunities."