After a tight first half when Carrick had the wind in their favour Belfast Royal Academy dominated the latter stages to qualify for a home tie against Sullivan Upper in the fourth round.
Academy, who eventually scored seven ties, took the lead after 15 minutes when Daniel Dass broke away to touch down but they only managed one more try before the interval as their opponents kept in the tie with two Keelin Gilpin penalties.
These came after the Carrick pack had driven downfield and used the elements to their advantage with kicks into the corner.
Towards the end of the period Academy mounted a number of attacks but poor handling prevented them from increasing their 12-6 lead.
In the second half Carrick suffered in the line-out and also gave away a lot of penalties at the breakdown.
Full credit to them as they stuck to their task and performed well considering they fielded seven fifth formers. Scott Henderson, Adam Urquhart and David Stewart gave their all up front and scrum-half Michael Black, with Christian Robinson and Chris and Rhys Berry, defended stoutly.
Academy had too many strong players and they managed a total of seven tries although some of those came in the final minutes when Carrick had only 13 on the pitch after two players were yellow carded.
Mark Wylie, Jordan Carlisle, Daniel McFadden, Stewart Martin, David Campbell and Sam Lindsay were the other try scorers for McFadden to convert three.
Carrick coach Gareth McClintock was pleased with his team's efforts. He said: “We were always going to be up against it but we fought hard and with so many young players in the squad it bodes well for the future.”
BRA coach Michael Creighton thought his side kept to the game plan and it worked.
“Carrick forced us to play our best early on but our strength told when we had the wind behind us in the second half,” he said.