With seven games remaining, the Swans appear clear of relegation danger, sitting ninth in the Premier League with 40 points.
A top-10 finish would complete a successful debut season for manager Michael Laudrup, who led the Welsh side to Capital One Cup glory last month.
Saturday's 2-1 defeat at home to Tottenham marked a third loss on the bounce for Laudrup's men and their poorest run this season.
But 30-year-old Britton says they still have objectives to fulfil this term, namely topping last year's 47-point haul, which saw them finish in 11th place.
"It's different if there's a cup final feel to things, it would be very different," he told the South Wales Evening Post.
"Maybe it might be the case that it does affect you in that way. But there's no way we're going into games thinking 'we're done, we're on the beach'. We're too professional to even think like that.
"We don't want this season to fall away, we want to finish as high as we can and beat last season's points tally."
The loss to Spurs at the weekend followed defeats to Arsenal and West Brom and Britton admits being the first team to concede has proved costly in recent games.
"No matter how we played and what we might have deserved, people will see those three defeats, but in all the games we've done well in spells," said Britton.
"It's not a case of us being abysmal and losing our way, we've just not performed as we can for the full 90 minutes.
"The lesson is that even in spells of games when you're not playing well, don't concede because in the Premier League it's tough to get back at any side."