The Swans travel to Anfield at the weekend to take on Liverpool on the back of the 3-1 home win over Bolton Wanderers, a result that lifted them to 10th in the table.
But they've yet to win away from home, and yet to take any points off any of the so-called 'big boys'.
"At Wolves we were ten minutes from picking up three points after a very good performance," 29-year-old Britton told the South Wales Evening Post.
"It wasn't to be but the next step is to get that away win because our home form has been very good.
"It would be great if we could do it against a big club like Liverpool at Anfield ? it would send a massive message out to the rest of the league and move us three points further away from relegation.
"We've played Manchester City, Chelsea, Arsenal, and it's hard when you go to these places.
"The next thing is to try to get three points against one of the big teams."
He added: "If you offered most teams a draw at Anfield before the game, they would take it.
"We will go and look to win but if we come away with a draw it's a positive result.
"We think if we play how we know we can, more often than not we will come away with a result."
Swansea last week