The Italy international appeared to overrule captain-on-the-night and designated taker Jordan Henderson to slot home the 85th-minute spot-kick, giving Liverpool??a round-of-32 first-leg lead.
It prompted the injured Steven Gerrard, a guest television pundit for the night, to accuse Balotelli??of being “mischievous” and disrespecting Henderson.
When asked to clarify who should have taken the penalty, Rodgers said: “I am clarifying we won the game 1-0. I have a number of outstanding penalty takers with Jordan and Mario and Rickie Lambert.
“We won the game. It was an excellent result and performance and it was always going to be a tight game.
“I believe Besiktas have scored in every away game so it shows our defensive organisation we kept a clean sheet.
“Simon (Mignolet) had an outstanding save in the first half. We created chances and moved the ball quicker in the second half.
“It was the perfect result and sets up for the second leg next week.”
Besiktas boss Slaven Bilic was disappointed his side could not hold out but he was far from downbeat.
“Of course when you concede a late penalty, late goal, you are gutted and from our point of view it wouldn’t have been unfair if it finished 0-0 or 1-1,” he said. “We deserved a bit more but from their side they deserved maybe the one goal.
“From the bench they had really class players like Balotelli and (Raheem) Sterling. It is a game of two legs. We definitely have a chance at home in one week’s??time to go through.”