The hosts looked set to be heading for a goalless draw in the first leg of the last 32 tie at Anfield, until Jordon Ibe was fouled in the area with seven minutes to play.
Substitute Balotelli - a clinical penalty taker - stepped up to convert the spot-pick, despite stand-in captain Henderson initially appearing set to take it.
Daniel Sturridge looked unimpressed by the incident and a further stir was caused when injured captain and regular penalty taker Steven Gerrard, working as a pundit for the game, revealed Henderson would have been the designated taker.
Rodgers, who initially passed no comment on the issue, said on Friday: "There's been a drama, a lot more made of it than it actually was.
"Of the players who were initially on the pitch, Henderson was penalty taker. But when Mario or Gerrard are on, they usually take them.
"What you don't like to see is the etiquette, four or five players around a football for the penalty.
"It's the responsibility of Jordan [to make the decision], if he feels Mario can take the penalty...Jordan gave the penalty to Mario.
"I always assign responsibility every game. If you're vice-captain and captain comes on pitch you give them the armband, it's a similar thing."
