Spencer joined Bath in 2020 after nine years with Saracens where he won seven major trophies – including four Premiership titles – through the London club’s era of dominance.
The 32-year-old was made captain in 2022-23 as head of rugby Johann van Graan’s tenure at Bath began, just months after the club had finished bottom of the league the season before.
“The amount of hard work this has taken to turn the ship around… we were bottom three years ago,” added Spencer.
“I can’t credit [Van Graan] enough, he’s been absolutely brilliant. If we [understand] there’s always an opportunity to get better then I’m really excited for the next couple of years.”
Bath narrowly lost to Northampton in the Twickenham showpiece last June but were overwhelming favourites this time around.
They ended the regular league campaign 11 points clear at the top of the table and wrapped up top spot and a home semi-final in the play-offs with three rounds of games still to play.
Scrum-half Spencer said he mainly felt “relief” at the final whistle because of the prolonged build-up.
“To get the mindset right when you qualify early as we did is quite tough,” he said.
“I played that semi-final in my head hundreds of times. Day in, day out it was, ‘who are we going to get?’ It’s a hard place to be mentally.
“It’s relief for me, the players, staff and fans.”