The Swans take on League Two side Bradford in the Capital One Cup final at Wembley on Sunday and midfielder Britton is ready for the challenge having come up through the divisions himself.
"A lot of the boys have played lower-league football so we know what to expect," said the 30-year-old.
"Myself, Monks (Garry Monk), Ash (Ashley Williams) and Tatey (Alan Tate) are used to that level of football. It's tough.
"For some of the lads, the boot was on the other foot six years ago. We were the team trying to beat higher division teams.
"But cup results this season have shown that anything can happen on the day, so there's no way we will be complacent. I am really looking forward to it, the first major cup final in the club's history."
Fellow midfielder Ki, a summer signing from Celtic, is used to the big occasion but admits he has experienced both sides of the coin.
Ki scored as Celtic won the Scottish Cup final against Motherwell in 2011 but suffered a shock defeat to Kilmarnock in last season's Scottish League Cup.
"When it comes to cup finals I suppose I have mixed emotions," said Ki, quoted in the Daily Mirror.
"It was great to win the Scottish Cup. The atmosphere was amazing and it is a brilliant feeling to win a trophy. But when you lose a final, it is horrible. You never want to experience that.
"We have a chance to become the first team in Swansea history to win a major trophy and that adds even more incentive for us."