O'Connell, who had made two substitute appearances for Rotherham since arriving on loan from Blackburn at the end of November, was one of two changes Evans made to his starting line-up for the 3-0 second-round replay win at Meadow Lane.
The 18-year-old was replaced late in the second half, but received a glowing appraisal from his manager.
"It was just cramp," said Evans. "The young lad has come from academy football where our scouting staff has seen him, they work round the clock going to games every night.
"We never sweat when we lose a player because we always know where another player is, but that is our job.
"I think we've had five left-backs this year, but everyone seems better. I think young Jack and his family will go home and be proud of his performance."