Everton managed to hold QPR 1-1 at Loftus Road yesterday.
Moyes said: "It was going to make it difficult to win when it went to 10, but I think we still tried to counter-attack at the right moments.
"It was a big game for QPR as you could see so we knew what we had to deal with. I think the players' did a really good job and kept the momentum going and made sure we got a result today.
"I think they will achieve more at QPR, they have a really experienced team. I have seen them play a couple of times and the players they have had great experience.
"I think they have got good players, when you bring in an awful lot of new players it can be difficult.
"They need to give the manager time. They worked hard for Mark today and tried to get a result."