The Swans begin their campaign with a trip to Manchester City on Monday night.
However, despite a tough start, England under 21 international Sinclair has revealed that Swansea will surprise some people this over the next few months.
"Everyone's expecting us to lose, I think we will surprise a few people and a few teams," said the winger.
"I think it's a good thing we're the underdogs going into games. Everyone's writing us off right now. Every time we go into a game there's no pressure whatsoever.
"We can't get criticised [for] what we're doing doing because they're writing us off already."
Sinclair was the Swans' top goalscorer last season, finding the net 27 times.