Dozzell headed in Liam Feeney's cross in the 1-1 draw at Sheffield Wednesday.
"He had two efforts in the old v young game on Friday. One, Gerks (keeper Dean Gerken) came out and was going to punch his head off," said McCarthy.
"The next one he thought Gerks was coming and got worried and missed both, so I teased him about his headers."
McCarthy continued to BBC Radio Suffolk: "But the nice thing was he was trying to head them on Friday and done them again in the match. He'll remember that goal for the rest of his career.
"I still remember scoring on my debut but it was in the League Cup against Chesterfield at Oakwell when we were in the fourth division. It stays with you."
Dozzell's father Jason became the youngest goalscorer in the top flight 32 years ago when he also scored on his debut, for the same club, at the age of 16.
And McCarthy, whose side are now eight points off the play-off places with just four games to play, says the England Under-17 international midfielder has the right attitude.
"His dad Jason's a coach and they're a nice family, he's got his feet on the ground, there's no flash about him at all," said McCarthy.
"He is a kid but he plays with a far greater maturity than a kid."
Ipswich Town manager Mick McCarthy teased Andre Dozzell about his training ground headers before the 16-year-old nodded home on his senior debut.