The Welsh side currently sit 15th in the Premier League table after a run of eight games without a win, although in that time they have knocked Manchester United out of the FA Cup.
This is in stark contrast to last season which saw the Swans finish ninth in the league and lift the League Cup, the club's first piece of major silverware.
Britton admits there is a big difference this season compared to the last campaign and is calling for everyone to stick together as they go through this tough period.
"We need to make sure we all stay together in this difficult period," he said.
"Of course the place isn't as bouncing during the week as it would be if we had won a run of games. So you just have to keep your chin up."
After enjoying success initially under Brendan Rodgers and then Michael Laudrup, Britton admits that it has been tough to adjust to this difficult time.
"At this stage in the last two seasons we have been looking up rather than down but now we're looking over our shoulder and only three points off relegation.
"We've got good experience in the changing room and that's important to pull each other out of this tough time."