"It's great, it's a great competition and a great chance to win a trophy. We're delighted," Cole told Sky Sports 1. "Everton are a top side, all credit to them, they always give us a great game but we wanted to win and we showed that.
"We've been on the end of a few bad semi-final experiences in Liverpool but it will be a nice flight home tonight. It was a good performance."
Chelsea had been under pressure before Cole converted Florent Malouda's superb long pass and the England midfielder added: "We needed it, we were under a lot of pressure.
"We stick together from back to front. Everyone defends and attacks together."
Chelsea manager Avram Grant paid tribute to his squad, which has been ravaged by injuries and the loss of players on African Nations Cup duty.
"It's a big test of character and the players are doing a great job," Grant said on Sky Sports. "I said we had a good squad. What they did today and in the last month was amazing.
"I'm excited to win any game. This competition is not a major competition but any trophy we can take we will do everything we can."