The versatile Wales star captained the Blues in their narrow Judgement Day defeat to the Ospreys at Principality Stadium.
But Anscombe is well aware of how big the game with Gloucester in Bilbao is for his team.
“It would be great to end the season with silverware, the club has gone through a tough patch over the past three to four years, certainly since I’ve arrived,” Anscombe said.
“We’ve had a lot of coaches coming and going and I guess some background noise, but this group has stuck tight and gelled and it’s really starting to show now.
“Even with the performance against the Ospreys, with a team that most of the media probably would have written off, we showed we were more than capable of winning that game.
“We’ve grown nicely in the last 18 months. Gloucester are a strong side and it’s going to be a tremendous occasion, but this group can be excited and feel we can give it a good crack.”
Blues boss Danny Wilson gave some of his key men a rest against the Ospreys with Bilbao in mind.
But Wales’ capital region showed they are heading in the right direction as their opponents had to rely on a late Dan Biggar drop goal to seal victory.
Anscombe hopes his battle with international team-mate Biggar will stand him in good stead for what will be a huge final in northern Spain.
The try-scorer against the Ospreys said: “It was nice to be back in the No 10 jersey. We were disappointed not to win the game, but we showed a lot of attitude and character in the second half.
“Our young boys stood up and put in some big shifts and it was nice from a personal point of view to get a try on Judgement Day as they have been few and far between this season.”
Anscombe continued: “Biggs went well and scored a nice try too.
“He’s been one hell of a servant to Welsh rugby and to Ospreys. He’s one hell of a competitor and he’s been the number one No 10 in Wales for a while.
“It’s always nice to compare yourself and get a chance to compete. He deserves a big send off from Ospreys because he’s done a hell of a lot in that black jersey and he’s a good guy, too.
“It’s funny when you spend eight or nine weeks together as mates, then you have to cross the whitewash and run in to each other for 80 minutes.
“He’s been a great servant to Welsh rugby and it’s nice to get some game time against him as well.”
Anscombe is equally comfortable playing at both full-back and fly-half.
Wales face South Africa in Washington and two Tests with Argentina this summer.
“The selectors know where I’d like to play, but in international rugby any time you get the opportunity to pull on the red jersey you have to take it,” Anscombe said.
“I think my skill set suits more at No 10, but at the same time I think I have the ability to do a job at No 15 and it’s a role I also enjoy, so it’s not like I’m going to put myself in a pigeon hole and say I can play only one position.
“After a few discussions in the Six Nations with the people who matter I think they know where I’d like to play and I’ve had some feedback, too.
“I thought the Six Nations was pretty positive from a personal point of view. I had a few more minutes than I’d had previously. I feel I’m building nicely and I just need to keep working hard.
“But as long as I’m involved, I’m pretty happy and we have a pretty special occasion with the Blues coming up.”
