"To lose Tom Cleverley through injury and to get a reaction, a flare up from James McCarthy is a real negative," Martinez told reporters after the game.
"It was a blow to lose James so early. We felt we needed an extra energy and you saw that with his impact in with the assist for the first goal.
"Tom then felt his Achilles tendon and we will have to assess it. He tried to stay on as long as he could.
"He played the pass for Romelu Lukaku for the second goal but he had to come off. He made a really big impact when he came on and he was playing a massive role."
Everton twice came from behind to lead 3-2 with 10 minutes remaining, Romelu Lukaku leading the way with a brace.
But a weak punch from goalkeeper Tim Howard and a rash challenge by John Stones, which led to the winning penalty in added time saw the Potters snatch the three points from the jaws of defeat.
"It is the hardest thing to do, to get back on level terms, then get ahead. It was a real blow to lose the third goal but clearly we have to become stronger defensively," Martinez said.
"There are certain actions we have to defend a lot better and, as a team, we have to get more mature. We have to be wiser in protecting that lead."
Everton, who are 11th in the table, host third-placed Tottenham Hotspur in the league on Sunday.
(Reporting by Shravanth Vijayakumar in Bengaluru)
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