Pep Guardiola said the “sacked in the morning” taunts started at the Amex.
But he added he expected better from fans at Anfield.
Liverpool supporters targeted the Manchester City boss as his side headed to a 2-0 defeat.
The result means the fourth-placed Seagulls are two goals ahead of the slumping champions in what is a congested Premier League table.
Guardiola clearly remembers being teased by Albion fans as their side beat City 2-1 recently.
He said: “I’m so proud of my six Premier Leagues against that team (Liverpool) and the previous teams.
“I didn’t expect Anfield to start to chant at 0-2 that I would be sacked.
“Maybe I deserve to be sacked, honestly, with our results, or maybe I’m still in the job because I won six Premier Leagues and a lot of titles!
“But I didn’t expect them to sing at 0-2. Maybe they should sing at 0-1 when the game was tighter or maybe last season or the previous season.
“Maybe in Brighton they did it, so I understand, but at Anfield I didn’t expect it. But it’s fine.
“It’s part of the game. When you win, you laugh, when you lose, they laugh. I have to accept it.”
Albion, who were joint second with City immediately after the 1-1 draw with Southampton, dipped back below Arsenal and Chelsea over the weekend.
They are just one win clear of Brentford in eighth with four teams a further one point behind.
Action resumes on Tuesday when four of the bottom seven are involved.
Ipswich host Crystal Palace and Leicester are at home to West Ham.
Wednesday’s game between Manchester City and Nottingham Forest will see one of those sides go above the Seagulls in the standings whatever happens.
Brentford go to Aston Villa on the same evening and Tottenham visit Bournemouth on Thursday, when Albion are at Fulham.
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