The Swans have drawn their first two home games of the season against Wigan and Sunderland, earning plaudits for their performances despite only taking two points from a possible six.
After scoring 27 goals last season for Brendan Rodgers’ side, a lot was expected of the 21-year-old but he, along with his fellow team-mates, are yet to find the net this season.
However, Sinclair is confident goals will soon come.
He told the club's official website: "The fans have always been brilliant with us - no matter what the score is.
"Against Arsenal last weekend, all we could hear were our fans singing away and supporting us. That's what every player wants to hear, particularly at an away ground.
"A lot has been made of the fact we haven't scored yet, but I'm sure with another sold-out Liberty on Saturday the fans can cheer us on to victory."
"At the Liberty it has been absolutely incredible. Against Wigan and Sunderland the place was absolutely rocking and we were unlucky not to score and win those games.”
"They key thing is that we are creating chances. If we don't do that then it's time to worry.
"But we've created chances in our games, and it's a matter of time before we take one.
"When that happens, I'm sure the goals will flow."
He added: "I've been disappointed with myself because I'm yet to score after getting 27 goals last season. But I've hit the crossbar twice and I'm getting closer.
"Danny (Graham) has gone very close too, and once he gets a goal he'll score plenty more because he is a quality player.
"But I look around the team and I see goals - not just from Danny, myself, Leroy (Lita), Nathan (Dyer) and (Stephen) Dobbie, but from the back and midfield too.
"We don't just look at the forward players and say 'it's your job to score' because it's not. We defend as a team and attack as a team - everyone has to chip in.
"But we're all confident and feeling positive about things. That's very important.
"Hopefully we can get a goal and three points on the board on Saturday because the team and supporters deserve it."