Swindon got off to the worst possible start when Franck Moussa gave Coventry the lead after just 64 seconds.
But the visitors controlled the game and Andy Williams equalised five minutes from time before Darren Ward headed a 90th-minute winner.
Carsley said: "I think we got what we deserved.
"After a great start we were below par in too many crucial parts of the pitch.
"I felt we were second best at times and that has nothing to do with tactics, technique or the pitch, it was just the mentality to win the personal battles.
"They set up a little bit different to us so at times it looked like they had more midfielders in there.
"Teams do tend to pack the midfield away from home. It's that last one per cent that ultimately we are all going to be judged on.
"For 99 per cent of the time we defended really well, but that one time we switch off, don't win the first header and don't react quick enough to block the shot then it ends up in the back of the net.
"It's no good defending for 44 minutes of the second half."