“It’s an amazing achievement.
This competition was a big part of the reason I wanted to come and play in France. We knew it would come down to the last minute because Leicester are a quality side, very fit,” the 34-year-old Carter said.
“Winning the final would be a dream come true. It’s been an amazing four and a half months, but that would top things off. Saracens are a quality side, the form side of the tournament, but I’m looking forward to it.”
Racing scrumhalf Maxime Machenaud barrelled over the line from close range following a storming break by former New Zealand winger Joe Rokocoko to give his side an early lead.
Carter converted a penalty to extend the French side’s advantage and, after Freddie Burns and Owen Williams had got Leicester on the board from the kicking tee, the former All Black struck again to put Racing 13-6 up at halftime.
Williams, on as a replacement for the injured Burns, slotted over another penalty as Leicester started the second period strongly before Carter restored Racing’s seven-point cushion.
Centre Johan Goosen finished off a flowing Racing attack but the effort was disallowed for a forward pass early in the move and although Leicester enjoyed plenty of possession, they were unable to break down a disciplined and organised Racing defence.
Goosen landed a long-range penalty to put the French side 10 points ahead and winger Telusa Veainu’s last-minute try proved in vain for twice former champions Leicester.
The final is in Lyon, France on May 14 and a new name will be on the trophy.
Saracens reached the final in 2014 but lost 23-6 to French side Toulon, the European champions for the last three years.
(Writing by Ed Osmond in London; Editing by Toby Davis and Ken Ferris)