Rodgers had highlighted the threat posed by Di Natale in the build-up to the game.
When asked about the inspirational performance the 34-year-old, the Liverpool manager said: "The guy has qualities, there is no getting away from it.
"It was a very good finish for the first goal. With the third I think we gave him a wee bit too much time, but he is a quality player.
"But I'll always only concentrate on my own players and where they can improve and be better.
"They give me and the team everything, but at critical moments of the game - in particular at the start of the second half - we needed to be solid and tight, and we gave away three goals."