The Swans were held to a goalless draw at Fratton Park and are six points behind second-placed Norwich with three npower Championship games remaining.
Rodgers' side are now without a win in three, but the former Reading boss is confident they can get back on track, starting with a home clash against Ipswich on Monday.
He said: "It's possible. You can only win your games and we go into Monday in a really good frame of mind.
"We'd have liked to have won, but it was important we stopped a wee bit of a rot which had set in. Now we go into Monday with big motivation to get three points and we'll just see what happens.
"We'll win our games and hope the others slip up. You can't rule it out. You never know. Teams have gone on winning runs. You know the impossible in football can become possible."
Source: PA
Source: PA