The Blues took the lead at Old Trafford through Didier Drogba and looked set to secure all three points in the fixture, until Robin van Persie struck in stoppage time to earn United an important point.
Courtois told reporters: "Of course it was frustrating because we controlled the game. But the table says we are the team to catch, that's true.
"If you look at how the game went, it's normal that we were not happy with a point and that says a lot about the way we're playing this season.
"We're doing very well and will try to continue like that and keep on winning. We have had two difficult away games in Manchester and have to go to Liverpool in a couple of weeks, hopefully we will get a good result there and then we have had a good start."