The Scot punished some poor defending to put the Blues ahead but the visitors were much improved in the second half and grabbed an equaliser through Michael Owen.
McFadden said: "We were by far the best team in the first half. They were the better team in the second half but if we take our chances it's a different game.
"They've done well to come back into it and in the end we've done well to hang on."
McFadden pounced on an error by Abdoulaye Faye after 33 minutes before beating Steve Harper - but he admitted he did not think the goal would stand.
"I thought I was offside," he added on Setanta Sports. "But I've cut across the front of the defender and managed to put it away."