Midfielder McCarthy was replaced at half-time following a crunching tackle by Johnson as Wigan lost for the fifth time in the last seven matches to remain in the bottom three.
Martinez said: "It was a nasty challenge, one incident off the ball. The referee has seen it and has given Johnson a yellow card. It is one of those actions you don't want to see. James McCarthy has been in good form and they took him out of the game, which is very disappointing.
"It is his ankle ligaments, we will X-ray it and get the results from the scans very shortly but I doubt if he will be available for the next 10 days."
Anthony Pilkington set the home side on their way with a well-taken effort after 15 minutes, only for Wigan substitute Shaun Maloney to level at the start of the second half.
However, Wes Hoolahan, who has agreed an extension to stay at the Norfolk club until 2015, arrived on queue after 64 minutes to head past Ali Al Habsi.
Wigan have several key men missing through injury, notably in defence, and Martinez felt his team had simply failed to get themselves a foothold in the match.
"Our start was sluggish and pedestrian, we were very, very, very poor and had our goalkeeper to thank for keeping us in the game," he said.
"The second half was very different, we started to control the game and Norwich had to start to defend. We scored a beautiful goal and were starting to build positive momentum, so our disappointment is the smallest man on the pitch gets a free header in the six-yard box.
"I felt with our second-half performance we merited something out of the game but it was a self-inflicted defeat."
- Sports & Recreation