The Swans are looking to make it two wins in a row after seeing off Reading in the League Cup on Tuesday.
Their last appearance in the topflight also left some positives as they held their own to force a goalless draw away at Tottenham Hotspur.
“Confidence is building after some good results – we had a goalless draw at Spurs and the victory at Reading,” Ayew said, as reported by his club's official website.
"But now we have to do the job on Saturday for it to be a great week.
“Hopefully we can make our fans happy. We have had some good results away from home but now we want to do it at the Liberty.
“We go into the Watford game with some confidence. We have good momentum. Now we have to play some good football and try to earn some points.”
This campaign, Ayew has made five league appearances for Swansea, who currently sit 14th on the table.
With one goal to his name, the former Aston Villa forward has already equalled last season's league tally for the Jack Army, having found the back of the net in a 2-0 triumph at Crystal Palace last month.
The 26-year-old has also netted twice in the League Cup thus far this term.