Dejan Lovren bundled home an equaliser a minute from the end of normal time to earn the visitors a 1-1 draw at Old Trafford after the Reds had gone ahead through Robin van Persie's first-half strike.
Moyes was pleased with some aspects of the performance, but felt that his team didn't have enough control of the game.
"We’d done enough to get ourselves more than one goal, but we never really had enough control at times. I thought we had really good pockets of play at some points of the game, but not enough control," the manager told MUTV.
"It was great to get off to a good start with a goal early on. I was impressed by Adnan [Januzaj], and it ended up with Robin getting a goal. We had chances to make it two - we hit the bar, but I said to the players at half-time ‘this won’t be enough, we have to do more’, and that turned out to be the case.
"We’re aware of what we have to do [to bounce back]. We’ll get ready to go again, starting with the next game against [Real] Sociedad.”
Moyes felt tiredness played a part as the game went on with those players involved with their countries in the last couple of weeks feeling the effects of the games and travel.
"The boys who had been on international duty looked tired, and it was on my mind, but I didn’t want to make too many changes before we got the game out of sight," explained Moyes. "As it was, we didn’t, and conceding in the last minute was a real sickener."