The 30-year-old played a key role despite Swansea throwing away a 1-0 lead to draw 1-1 at Ashton Gate.
Swansea took the lead through forward Jamal Lowe in the 51st minute, but a late surge from Bristol City saw them level in the 83rd minute after Nakhi Wells converted from the spot.
"Good fight, we keep going, back at the Liberty on Tuesday," wrote Ghana's captain on Twitter.
The Welsh club will host Stoke City on Tuesday, with the hopes of returning to winning ways.
Swansea City have lost just a game in the Championship this season, and are currently fifth on the table.
Ayew, who was last season's top scorer is poised on leading the club back to the English Premier League after reaching the playoffs last season.
Read Full StoryGood fight today , we keep going ????????..back at the Liberty Tuesday ???? YJB pic.twitter.com/SmzY61AbAb
— André Ayew (@AyewAndre) October 24, 2020
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