The Italian was withdrawn before the second half began after an ineffective first period, and the Reds boss explained why his £16m striker was swapped for Adam Lallana.
Rodgers told Sky Sports News: "[Balotelli's withdrawal was] tactical. I felt we needed more intensity thorough the middle and occupy their centre-backs more and Adam Lallana come on and did well there. Young Raheem Sterling was playing there and did well, he kept working hard and I thought he was excellent."
Balotelli came under fire in some quarters after appearing to swap his shirt with Madrid defender Pepe as both players walked down the tunnel at the end of the half, and Rodgers said that he would be looking into the incident.
"That's the first I've heard of it but if that's the case then I wouldn't like it either," Rodgers added. "I don't like to see it and I've seen it happen in other leagues and countries.
"It's something that doesn't and won't happen here, and we had an incident last year where I dealt with a player [for swapping shirts] and if that's the case then I'll deal with this as well."
The defeat leaves Liverpool third in Group B.