Following their 2-1 defeat at Burnley on Saturday, the Swans are five points adrift of second-placed Cardiff with four games remaining in the npower Championship.
But midfielder Britton remains hopeful they can clinch second place.
He told the South Wales Evening Post: "It's not over. You've got to keep going until it's mathematically impossible.
"It was very quiet in the changing room at Burnley and people were angry as well.
"There's no point dwelling on things. We've got two games in three days next weekend, which is a good chance to pick up six points in a short space of time and try to kick up the table."
Source: PA
Source: PA