Substitute Robert Koren netted the winner for the visitors seven minutes from time after Anthony Wordsworth had cancelled out Robbie Brady's penalty.
McCarthy said: "We endured a tough first half and I had to change things around to try and stop them playing.
"It was working until the penalty and after they scored it gave them a bit of freedom and confidence. They were far better than us in the first half but in the second I thought we were dominant.
"We deserved our equaliser and had the better chances to win it, but it's no good being the dominant team and then getting beat.
"We didn't defend the corner particularly well. It was a mistake for the penalty and a mistake from the corner. But we should have repaired it. There's no point compounding a mistake with another mistake."
Of his side's fight to avoid the drop, McCarthy added: "From day one I thought it would go down to the wire.
"This set of results were another mixed bag. It's a strange, strange league. I still think 56 points will do, but I don't get everything right!
"My attitude has always been to keep calm, carry on and take it one game at a time. That's been my attitude since November 1. Nothing has changed. It won't be easy but I've never done anything the easy way in my life."