"It could come down to Anscombe having a kick a goal with a minute left to win it for the Blues and knock the Ospreys out," said Jarvis, who struck an issue after signing for Neath from Pontypridd.
"Personally, as a coach, I wouldn't want to put that pressure on him.
"What would I do? I most probably wouldn't play him, if I'm honest.
"It's a difficult one to call. But, put it this way, when I was left out of that Ponty-Neath game, I was relieved."
The Champions Cup is the premier competition for clubs from the countries who compete in the Six Nations.
But whereas Jarvis was left out, Cardiff coach John Mulvihill is adamant the 27-year-old Anscombe will play.
"He's one of our best players so he'll play - he's a complete professional," insisted Mulvihill, according to Wales Online.
"If there's a 50/50 ball or a goal to be kicked, he's the man to do it. It may be the Gareth Anscombe show.
"He's had a great season with us and wants to finish on a high.
"Players and coaches come and go and we happen to be playing the Ospreys this week.
"Gareth will want to leave Cardiff Blues on a high and I have 100 per cent confidence in him."
Osprey's coach Allen Clarke also said Anscombe would do his utmost to win.
Clarke said: "We will do things the correct way. Gareth is a good man who has great integrity – that was part of the attraction of signing him."
Anscombe, who played for the Blues and Chiefs in Super Rugby, will reportedly play at fullback.
