Ayew was on parade for the entire duration but could not add to his tally of three goals in seven league matches this season as Steve Cooper's side settled for their second straight draw in the English second division.
Jamal Lowe gave the visitors the lead at Ashton Gate with his 51st-minute finish but his opener was cancelled from the penalty spot by Nahki Wells' equaliser for Bristol seven minutes from time.
Ayew managed one of the two shots on target registered by the Swans in the entire game and he also received a yellow card for taking his protest against referee Oliver Langford too far in the 87th minute.
The draw saw Swansea City drop to sixth in the Championship standings with 12 points after seven matches while Bristol City remain second with 14 points.
At the end of the encounter, Cooper said Ayew and his teammates were gutted by the result after their ‘decent display’ on the road.
“The lads are really disappointed with a point because of the nature of the equaliser and the decision on the penalty,” Cooper told the club website.
“I thought it was a decent game, I liked our performance coming away from home and being as positive as we were and committing bodies forward when we could.
“We got the opener, it was a great finish from Jamal, and we looked comfortable.
“I thought we would go and on and win the game and score another goal rather than seeing the game out.
“Then, when a decision like that is made, it’s hard to keep your mouth shut on it, to be honest.
“That decision, there is nothing you can do to make it better. There’s nothing you can coach or say or do in preparation to make that better.
“It’s so hard to get points in this league, so to get a decision like what when we were so comfortable in the game. It’s a difficult one to take, to be honest.”
Ayew will be aiming to return to the score sheet when Swansea City host John Obi Mikel's Stoke City at the Liberty Stadium on Tuesday.