Centre Brad Barritt said the “prospect of another week together” spurred Saracens to a 22-17 win over Leinster in their Champions Cup quarter-final.
The holders opened up a healthy lead before having to hold off a second-half fightback in Dublin.
Some players are set to leave Saracens next season after the club’s relegation from the Premiership, but Barritt says their “spirit shone through”.
“This team has been built on hard work, adversity and resilience,” he said.
Speaking to BT Sport, he added: “There has been setback after setback in our team, but the togetherness shone through.
“Physically, we wanted to be aggressive in every collision, with and without the ball. We won the contact against this Leinster team who have been formidable this season.”
The exodus has already begun at Saracens. Liam Williams has headed back to Scarlets while scrum-half Ben Spencer has joined Bath.
There have also been a raft of loan deals with Ben Earl and Max Malins joining Bristol Bears, Alex Lozowski moving to Montpellier and Nick Isiekwe heading to Northampton.
But former England centre Barritt, 34, said the remaining players “owed it to ourselves to represent the Saracens badge with respect and honour”.
“We know after this season we will have a slightly different-looking squad,” he added.
“Today was about fighting for something tangible and I could not be more proud of my team.”
Those comments were echoed by the club’s director of rugby, Mark McCall, who said his side “never ceases to amaze me”.
“They have been through so many experiences as a group and we saw that out there,” McCall told BT Sport.
“We showed the cohesion and unity out there to see it through. We needed to win as many little victories as we could today and put them in places they don’t have to go too often.
“This is what we have dreamed about in a difficult testing challenging year.”