Despite dominating possession and having more shots on goal than the visitors, United came away from the fixture empty-handed.
"We got done on the counter-attack for a couple of goals and made a couple of mistakes," Moyes said after the match, "but I thought the team played very well today.
"All you can do is play well and then hopefully you take your opportunities when they come and you don’t make small mistakes."
Moyes is adamant United "never deserved to be behind" and yet the players found themselves 2-0 down after 66 minutes thanks to Tottenham goals from Emmanuel Adebayor and Christian Eriksen.
Danny Welbeck halved the arrears inside a minute of Eriksen’s goal before the Tottenham side stood firm to repel wave after wave of United attacks.
“The players played very well,” the manager said. “Their effort was terrific to try and get back into the game after being 2-0 down.
“I actually thought when we got the goal back that we’d go on and win the game, never mind draw it; with the amount of chances we had, we really should have done so.
"We shouldn’t have been in the position of being 2-0 down. We’d already made a change to see if we could go for it a little more and get a goal back but their second goal was on the counter-attack.