The side may have started as second favorites to Manchester United, but they took a 2-0 lead at half time, only to find United getting an equalizer late in the game.
And Dyche believed the referee had a part to play in the result.
"We don't want to get too greedy. It's a tough place to come, we all know that. We gave a good performance overall, defended resolutely, did all the ugly stuff you have to do when you come to these places," he said.
"My only minor frustration is the late goal, but also the decision which led to it. I don't know what Sam Vokes is meant to do to try to not give a free-kick away, as he just stands his ground and the lad runs into him.
"We've seen a bit go against us this afternoon, but we've seen through that, and we've got a point on the table. I though the back five were excellent today, you have to be on guard here, that's for sure."