The Everton boss was disappointed not to pick up a win at the home of the champions but refutes suggestions that his side could qualify for the Champions League
Marouane Fellaini gave the visitors a well-deserved lead before conceding a penalty after pulling down Edin Dzeko in the box and the Scot feels that their seventh draw in nine games is evidence of a lack of cutting edge.
"I think it will be hard for us to make the Champions League. It'll be a big thing for us," Moyes told the Daily Mirror.
"I think we've got confidence and the players are playing really well. We're just lacking maybe getting over the edge.
"We're missing Kevin Mirallas, Victor Anichebe and we're just short of other forward options at times to maybe win us the games, that's why getting so many draws.
"I don't want to be a manager who keeps saying, 'We're playing well and not winning', because I'd rather be a manager whose team weren't playing well and winning.
"But the facts are there to see and we have to hope that good performances eventually lead to good results."
Moyes believes in his side's ability but has questioned whether they have the capability to match their top performances in a consistent manner over the course of the season.
Moyes continued: "When we play over 90 minutes against someone we've always got a good chance. But can we do it over 38 games?
"We should have more points. It's not been this point or the point against Arsenal; it's a couple of games before that where we've let winning positions slip to draw them.
"I think the game against Arsenal, as much as this one, shows we can have a go. But whether we'll ever have enough to be right amongst those teams when it comes to it...
"We're certainly not a million miles off them and we can be quite close to them."