The Reds boss kept his striker away from the City manager as the pair suddenly became incensed with each other.
Footage shows Guardiola and Nunez clasping each others hands near the dugouts at the end of the game.
Klopp then comes over to congratulate his striker, but Nunez and Guardiola's expressions soon change and they are both spotted shouting at each other.
The Liverpool manager continues to embrace Nunez and walk him away from Guardiola, but the Spaniard follows the pair, appearing to shout at the Uruguayan.
Guardiola is then held back by Liverpool's staff, as other members of the team, alongside Klopp and Curtis Jones, push Nunez off to celebrate with the away end.
MORE ON PREMIER LEAGUE
Haaland smashes Premier League record against Liverpool to leave legends in the dust
Everton fans' three-word protest banner spotted flying over Man City vs Liverpool
It is not entirely clear what Guardiola and Nunez were saying to each other or what sparked their row, but it was ultimately diffused.
Klopp and Guardiola were also later seen having a friendly conversation and hugging each other.
Nunez pointed at the badge on his shirt as he addressed the away fans, who were celebrating snatching a point in the closing stages of the game.
Trent Alexander-Arnold netted in the 80th minute to cancel out Erling Haaland's record-breaking strike.
Most read in Football
Everton fans' three-word protest banner spotted flying over Man City vs Liverpool
Haaland smashes Premier League record against Liverpool to leave legends in the dust
Man City 1-1 Liverpool LIVE REACTION: Spoils shared as top two serve up thriller
Why Brentford vs Arsenal is kicking off at 5:30pm as TNT Sports move London derby
Man City remain one point clear at the top of the Premier League, with Liverpool still hot on their tails in second place.