Curbishley is convinced Cole was marginally offside before he rounded Hammers goalkeeper Robert Green to score the only goal of the game at Stamford Bridge.
He said: "There were a couple of things. Carlton Cole thinks he should perhaps have had a foul trying to take Alex on. And it (the offside call) was tight. I think he (Joe Cole) was perhaps slightly off and I have seen it again.
"But it was the linesman's decision and we have just got to get on with it. We just lost a bit of concentration. We lost the first header and Matty Upson got attracted by the second one.
"But it needed someone to pull something out and Joe Cole did that."
Chelsea manager Avram Grant was critical of the Hammers, claiming they had been over-physical, especially in the opening minutes.
He said: "In the first half we had to be busy reacting to their aggressive game, which we had been expecting, but in the second half we played our game and went on to win.
"West Ham were lucky they got only one yellow card in the first 20 to 25 minutes. They were very aggressive and more aggressive than us."
Curbishley hit back: "It was a local derby. There were some tackles, some niggly ones in the first half especially, but we were probably on the end of the two worst ones."
Grant also labelled the visitors as too defensive, having made the short journey across London in search only of a goalless draw.
But Curbishley insisted: "I came here to match up to stop them dictating the game - which is what we did. But perhaps I didn't have enough going the other way.
"If we had got out of here with a point I think most people would have agreed that was a fair result.
"We did a really good job defensively and that was why I was so disappointed with the goal.
"We didn't really fashion any chances to test their goalkeeper so in the final third we didn't have enough but I'm delighted with the way we performed."