After winning 23-6 in appalling conditions against bottom side Glasgow, the Ulster coach praised his squad's efforts but called for one more major effort in France next week.
"There was a job to do (against Glasgow) and we did it," Anscombe said. "I'll certainly take a 23-6 victory and credit to the guys they hung in there and I thought they finished the stronger and scored a couple of tries."
He added: "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."
Tries from Nick Williams - who is already a doubt after picking up a knee injury - Jared Payne and Darren Cave along with a conversion and two penalties from Ruan Pienaar sealed the four points.
And Anscombe is already thinking about taking on a Castres side who have won three of their five games in the group, but can't qualify for the knockout rounds.
"We set out as a goal this year to make a Heineken quarter-final," he added.
"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."
Ulster skipper Chris Henry agreed and made another victory the essential focus for the squad.
"I think the players know what's at stake now to make a home quarter-final," he said. "We've given ourselves an opportunity and now winning in France is our goal. It's a massive focus for us."
- Sports & Recreation