The midfielder scored the winner against Aston Villa and insists they are firmly behind manager Garry Monk despite contrary reports.
The Ghanaian midfielder scored the winner on Saturday afternoon, as he got on the end of a Kyle Naughton cross to finish past Brad Guzan and secure all three points for his side.
He has now scored five goals in eleven appearances for Garry Monk’s side since joining on a free transfer from Marseille in the summer, and while he looks like being one of the signings of season so far, he has vowed that there is more to come from him.
"I believe if I continue to work hard I can do much more," he told BBC Sport.
"It's about getting to know the league better, getting to know my players better. They are helping me with that and giving me the confidence. I'm sure with time I can even get better."
The win was a big one for the Swans, as it ended a run of six games without a win, with them failing to secure a victory since beating Manchester United in August.
That run had seen them fall from fourth in the table to fourteenth, with reports suggesting that Garry Monk was under increasing pressure at the club to turn around their poor run of form.
Those reports were vehemently denied by Swansea though, and Ayew insists that he and the rest of the squad firmly believe in their manager.
"The manager never showed any pressure," he added.
"He stayed confident and believed in us. We also believe in what we do and believe in what he proposes to us in training. We have great confidence in our manager. That wasn't an issue at all.”