Martinez relieved Barry avoided serious injury
Barry completed the game despite being injured by a challenge from Cardiff defender Kevin Theophile-Catherine in the first half.
Theophile-Catherine was booked by referee Roger East but Everton's manager felt the Frenchman was lucky to stay on the pitch and highlighted the damage the tackle had caused.
"Gareth has stud marks on his shin," the Spaniard said. "It's a strong knock but it didn't affect any joints so that's the reason he could carry on.
"I haven't seen the replay, but I believe the player has both feet off the ground and he doesn't get the ball so it was a reckless, violent challenge."
Everton's official website confirmed that Barry would be assessed on his return to training.
The 33-year-old, who has played 23 times in the league this season after joining on loan from Manchester City, will hope to be available for Everton's home game against Swansea City next weekend.