The loss was a sixth in seven games for City, as the home support taunted Guardiola during the game with "you're getting sacked in the morning" chants.
In response, Guardiola would turn to the baying crowd and hold up six fingers, to highlight the six Premier League titles City have won under him.
The Catalan did the same at the final whistle to City's away support as a sign of solidarity.
Guardiola said afterwards: "ll the stadiums want to sack me, it started at Brighton! Maybe they are right with the results we've been having. I didn't expect that at Anfield.
"They didn't do it at 1-0, but at 2-0. Maybe they should have sung it in the past. I didn't expect it from the people from Liverpool but it's fine, it's part of the game, and I understand completely. We've had incredible battles together. I have a respect for them."
- Get breaking football news faster with the new Tribal Football app! Download now on iOS and Android to stay ahead of all the latest transfers and football updates. Download now: App Store, Google Play