The 30-year-old labelled the achievement "unbelievable" after the side defeated the reigning European champion over two legs, while Ashley Williams praised its solid defense
The Blues dominated possession but failed to breakthrough the hosts' solid defense, with Michael Laudrup's men also proving a danger on the counterattack.
The stalemate at the Liberty Stadium sees the Welsh outfit win the tie 2-0 on aggregate, after an impressive victory in west London, and sets up a final at Wembley against League Two's Bradford.
The midfielder insisted that the Swans had to be at their best in both games, but was delighted to see their hard work pay dividends as they set up a trophy chance.
"It's unbelievable tonight," he told Sky Sports. "To do it over two legs against a team like Chelsea, the team have been brilliant in both games. Tonight we made history, which it great for Swansea. You wouldn't dream it.
"Reaching the cup final beating Chelsea over two legs but the club has come on leaps and bounds in the last 10 years. It's great for the club, even in a sense of just reaching the final.
"I think we've been a bit more attacking this year. [Laudrup's] brought in some obviously brilliant players along the way. He's just took us on another level again and we keep on improving."
Though many will fancy the Premier League side to walkover its fourth-tier opponent in the final, Phil Parkinson's men have already knocked out Arsenal and Aston Villa and the Team GB star suggested it will not be straight forward.
"I think they've done brilliant," he continued. "In the lead up to the final they beat a few Premier League teams on the way and Villa over two legs. It's going to be a great day but a really tough one."
Ashley Williams, who was a rock at the heart of the Swans' defense on Wednesday night, agreed that the team got its tactics spot on, frustrating the likes of Juan Mata, Eden Hazard and Demba Ba, and praised the collective defensive effort.
He added: "At times I think it was like a bar fight when they were pushing on, but I think the team defended brilliantly.
"That's what we worked on. Obviously bringing them back here we wanted to score a goal and keep a clean sheet. We didn't score but we've kept a clean sheet and the job got done in the end."