Swansea parted ways with Michael Laudrup at the start of the month after struggling to build on last season's promising form, but new head coach Garry Monk has since taken four points from his two games at the helm.
The Welsh club, who marked Monk's dugout debut with a 3-0 win over bitter rivals Cardiff City, continue to fight on three fronts and Britton is excited at the prospect of progressing to the latter rounds of the FA Cup and UEFA Europa League.
"We have some very, very tough games now with Everton, Napoli and Liverpool, but at this level every game is tough," the midfielder said in quotes reported by the South Wales Evening Post.
"It's Everton first and it's something to look forward to. The FA Cup is a different challenge and we are going to a ground where the club has never won before.
"It's nice to have a break from the Premier League - we have done well in cup competitions recently – and then we play Napoli, so these are exciting times."
Swansea travel to Everton on Sunday in the fifth round of the FA Cup, before welcoming Rafael Benitez's Napoli to the Liberty Stadium in the last 32 of the Europa League four days later.
