The Welsh side have gone five games without a victory and face back-to-back tests against Champions League-chasing Chelsea and second-placed Manchester City.
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|13/8||Swansea are 13/8 with BetVictor to finish in the Premier League's bottom 10
"We've got some tough games but we've shown we can play and don't have to fear these teams," the 30-year-old told reporters.
"I'm sure we can pick up the points to finish in the top half, which was our target."
The midfielder also noted that everyone at the club was disappointed to see 21-goal team-mate Michu surprisingly left out of the nominations for the PFA Player of the Year award.
"We're a little bit surprised about the PFA awards," Britton remarked. "It would have been nice to see a couple of our lads recognised for what they've done, Michu especially, because he's been fantastic and you wonder where we'd be without him."