"This is an amazing achievement for the club and playing in the Champions Cup is part of the reason I came to play in Europe. It has certainly lived up to all the hype and reaching the final is huge for this team," said Carter.
"We knew it was going to come down to the last minute because Leicester are a quality team and really fit. I'm really proud at the way we held on to things and it has been an amazing four-and-a-half months in Paris already. Saracens have been the form side right from the first game, so we will have to prepare well for the final."
Nick Evans made a telling early return from injury to help propel Harlequins into the European Challenge Cup final with a 30-6 semifinal win over Grenoble in London.
The former All Black scored a try and kicked three goals off the bench, while Ben Botica, who started, also kicked three goals. Starting for Grenoble were Steven Setephano, Sona Taumalolo and Nigel Hunt.
Anthony Tuitavake's Montpellier are also through to the final, defeating Nick Crosswell's Dragons 22-12.
In the sole Aviva Premiership catch-up game, Bath defeated Sale Sharks, despite a brace to midfielder Johnny Leota and a try to TJ Ioane for the latter. Lock Bryn Evans also started for Sale.