"I am proud of the commitment of the team," McCarthy said after the game at Molineux.
"We took some time to get going and that might have been down to the fact that we played against Leeds United on Sunday.
"But I don't want to use that as an excuse as we were the better team in the second half.
"The fans stuck with us and the fact they were still there cheering us on at the end said it all to me.
"We could have got something late on but missing that penalty in the first half was a turning point as it gave Derby a lift and took the wind out of our sails.
"The players are disappointed but they should be proud of what they have achieved so far this season and we would have taken our points tally at this stage if we had been offered it at the start of the season."