David McGoldrick's late winner settled a gritty and hard-fought contest at Portman Road.
McCarthy said: "I'm delighted, relieved and glad it's over. It was a well-organised, gutsy performance.
"We weren't the best team by any stretch of the imagination but when it was required we had that little bit of brilliance of composure from David McGoldrick.
"It was a good, aggressive game. You'd expect that from Mick McCarthy and Nigel Pearson teams."
Leicester manager Nigel Pearson accused Michael Chopra of kicking out at Wes Morgan and then claimed Daryl Murphy elbowed the same player.
Of Pearson's moans, McCarthy added: "It got a bit fractious but the reality is that as a centre-half you have to keep your composure.
"There was a tangle of legs but whether he caught him or not I don't know.
"That upset the applecart a little bit but that would be the last of my worries if I was playing against Chops.
"I've got no sympathy with the centre-half. If it was one of mine, I'd be saying `you let him upset you and it's cost us the game'."