The match was a heated affair and the home side eventually edged out Leicester courtesy of David McGoldrick's 85th-minute strike.
"I'm delighted, relieved and glad it's over," Sky Sports News quotes McCarthy as saying. "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 McGoldrick.
"It was a good, aggressive game. You'd expect that from Mick McCarthy and Nigel Pearson teams."
The result moved Ipswich to 18th, six points clear of the relegation zone.