Latics midfielder James McCarthy had to be replaced at half-time after suffering an ankle injury following a crunching tackle by Johnson.
"It was a nasty challenge, one incident off the ball," said Martinez.
"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 gave Norwich a 15th-minute lead but injury-hit Wigan replied through Shaun Maloney on 51, only for Wes Hoolahan to seal victory for the Canaries on 64.
"Our start was sluggish and pedestrian, we were very, very, very poor and had our goalkeeper to thank for keeping us in the game," said Martinez.
"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."