The Red Devils had to twice come from behind to earn a point at Tottenham Hotspur yesterday, following on from their convincing 5-0 victory over Bayer Leverkusen on Wednesday.
Although Moyes said that he was frustrated with the dropped points, he hinted that he would have taken a win in Germany and a draw in North London at the start of last week.
"I feel we've dropped two points," the Scot told MUTV. "In normal circumstances, coming to Spurs, and it's been a tough game, you'd feel it was a good result.
"I think if you'd said to me before Leverkusen and today that we'd win in Germany and draw here you'd say: 'Hey, they are good results and it's not bad'. The disappointment is going back to last week when we drew at Cardiff.
"I'm concerned we're not as close as we'd like to be [to Arsenal] but it's a long season and hopefully we'll be there or thereabouts. There are a lot of games to go. I think the Premier League is tight and we'll try to stay on the shirt-tails and put ourselves in a good position at the start of next year."
Moyes welcomes his former team Everton to Old Trafford on Wednesday.