Martins joined Birmingham on loan until the end of the season from Rubin Kazan in the January transfer window.
Martins scored the winner for the Blues in the 2-1 Carling Cup final victory over the Gunners.
Carr said: “He showed that bit of sharpness when he came on. He’s a handful.”
“That will make their year, make their life probably,” Carr added on the passionate support from the Birmingham supporters at Wembley. “A lot of people have been waiting a long time for this.
“We knew if we got right in (Arsenal’s) faces we could get the result. We kept going and we just got that little bit of luck at the end.”