The 27-year-old defender returned to the starting lineup in the Blues' 6-1 Carabao Cup second-leg win at home to Middlesbrough on Wednesday.
Chelsea have, however, been beaten in their last three domestic cup finals, losing twice on penalties against Liverpool in 2022 and having lost the FA Cup final to Leicester in 2021.
Asked how he sees the upcoming final against Liverpool, who beat Fulham in their last-four tie, next month, Chilwell said: “It’s three finals we’ve lost, so 100 per cent there is unfinished business.
"I was, literally, five minutes ago talking to Thiago [Silva] in the shower and saying how we’ve got unfinished business at Wembley.
"We’ve both been there three times and lost three times, so, for sure, we want to go and win and, as a group, we need to make sure that we go and really enjoy the experience and soak it in.
"That’s equally important for a group like ours because there’s only a few of us who have won a trophy at Chelsea and it’s a club that demands trophies, so we need to make sure we go to win, but, also, it’s going to be a great experience for a lot of the players and they need to enjoy it as well.”
Chelsea's vice captain was excellent on his return against Boro, helping to set up the opening goal as the Blues won 6-2 on aggregate.
It was a particularly impressive display, given it was nearly four months since he last started a match.
Amid a run of injuries, including his latest hamstring issue, he said: "It is tough, of course, you want to be playing football.
"I’ve missed some great games of football, some games I’d have loved to have been involved in, but it’s important to focus on myself and just make sure when I get back I’m ready and that, mentally and physically, I’m in the best shape I can be in to help the team.
"Today was my first start and I was over the moon and very keen to try to give everything. I knew I wasn’t going to last the whole game, but it was more about seeing how long I could go for and giving everything into the game.
"It was a very important game for the club, going to Wembley, and I think for this group it’s going to be so important and a great experience for the team. We’re all looking forward to it.”