Clarke said: "We wanted to stay in the game as long as possible, but they managed to pull away with the two goals in the first half.
"That then makes it difficult when you are playing a good team.
"You can risk a little to try and get back in the game, but if you risk too much then you can end up doing serious damage to your goal difference.
"We tried our best to get back into the game in the second half, and even in the first we had some moments, some opportunities, we could have have created something, but didn't quite.
"It was a game where it had to go to 2-1, which at any stage in the second half would have given us a fighting chance.
"But the third goal from the penalty was a shocking goal to concede, and that more or less killed it.
"But credit to my players because we kept going and got our reward in the end with two late goals, which in my opinion puts a fairer reflection on the game."
Clarke, meanwhile, had no complaints with the two penalty decisions from referee Chris Foy.
The first was for Kolarov's tackle on Shane Long five minutes into the second half, and the second when Claudio Yacob brought down Kolarov that led to Toure's spot kick even though the midfielder appeared to get the ball first.
Clarke added: "Their penalty was a penalty, and the tackle on Shane, if given, would have been very soft."