Wednesday night's 2-0 win over Chelsea, which came courtesy of goals from Michu and Danny Graham, means Swansea are now red-hot favourites to reach their first major Wembley final in history.
"It's hard to describe how I'm feeling," Britton said. "It's up there as the best performances and results since I've been at the club."
Should the Swans see out the second leg at the Liberty Stadium - where they have lost just twice this season - it will provide another chapter in what has been a remarkable decade or so for the club.
Saved from financial oblivion by a local consortium in 2002, the Welsh side survived relegation from League Two on the last day of the following season, but from there it has been a success story, with the club climbing the leagues to reach the heady heights they now occupy.
And Britton added: "To go to the European champions, score two goals and not concede any with the attacking quality they have got is a great achievement for this club. Remember, 10 years ago this May we were beating Hull to stay in the Football League."
Yet before departing on the three-and-a-half hour coach trip back to south Wales, Britton was keen to sound a warning to his team-mates and the Swansea fans who are already dreaming of going to Wembley on February 24.
"We are halfway through this tie," he said. "I know it's boring, but we can't get complacent because we have 90 minutes to play at home against a team of Chelsea's quality."
Although Chelsea will rely on the likes of Eden Hazard, Oscar and Juan Mata to deliver a surprise comeback, the Swans know they have a more lethal weapon in their own arsenal. Michu, a £2million signing from Rayo Vallecano last summer, now has 16 goals to his name in all competitions.
Wednesday night's strike, which came after the first of two glaring errors from Branislav Ivanovic, may prove to be the most important of his career at the Liberty Stadium. Britton said: "For £2million I think, although Robin van Persie might be the signing of the season, you've got to say Michu is right up alongside him. The chance he had was still a tough one to put away but he's done it all season."
- Sports & Recreation