Despite that, Anscombe is desperate for Ulster to push on from the Glasgow win, with a success away at Castres absolutely vital if they are to earn a home quarter-final.
He said: "We set out as a goal this year to make a Heineken quarter-final.
"But we're certainly not resting on it and we're going to Castres next week with a job to do and a purpose to what we want to get out of that game and reward our fans with a home quarter-final.
"I think if we don't do that we'll have let the supporters down a little bit. We know where our work's going to be next week if we don't front up there.
"It's also credit to the guys that they've achieved this and that's one thing that we can put down that we've qualified after the fifth round of matches for the quarters."