Everton were beaten 3-2 by West Ham United last weekend.
Lennon was one of Everton’s brightest sparks against the Hammers, but Martinez chose to replace him in the second half with Oumar Niasse.
The decision was greeted with confusion at Goodison Park, and it backfired on the Spanish boss.
Everton had been in a 2-0 lead when Lennon was withdrawn from the action, but they folded after the England international winger went off.
West Ham scored three times in the final 11 minutes to claim a victory on Merseyside, but Martinez insists that his change was the right move.
“Aaron got to the point he was empty,” he said. “But we never felt the game was done. It was a case of fresh legs. Oumar is a very energetic player. The way we set up in the second half demanded a lot of effort from Romelu [Lukaku] and Aaron Lennon.”
Lennon has been in a wonderful run of form recently, and he has scored five goals in his last seven matches.
Everton’s defeat to West Ham has left them down in 12th place in the Premier League table, with frustrations continuing to rise at Goodison Park.
The Toffees have been guilty of throwing away leads in the latter stages of matches throughout the campaign, and their collapse against West Ham was simply inexcusable.
Martinez is now under severe pressure at the Merseyside club, with the Toffees’ next match coming against Chelsea in the FA Cup.