There was little to choose between the teams and Ipswich failed to take their chances before they were made to pay with 10 minutes left when the unmarked Scott Arfield stooped to head home Kieran Trippier's cross.
McCarthy said: "I don't think Burnley were any more accomplished than us but they had a Johnny-on-the-spot who came in and scored.
"We got what we deserved as they defended their goal better than us for the 90 minutes.
"I was delighted with how we played against a very good side but are they better than us? I don't think so.
"They just have people who are putting the ball in the net and there were three or four tiny little areas which led to their goal.
"We are not that far away. There is not a great deal between us and Burnley."