Wales’ record-breaking 40-6 victory over Australia meant they got the job done early in Pool C.
They preserved their 100 per cent record with one game still remaining – against Georgia next week – leaving other teams, led by Fiji, to fret over reaching the knockout phase.
Had Wales lost, it would have been a different story and meant them being caught up in a nervous scramble for two available places.
“It is probably relief. I don’t like that saying that, but we knew there was a lot on it,” Wales fly-half Anscombe said.
“We knew if we didn’t win we would go into the last week not quite having control. It is really rewarding because we do so much hard work.
“We’ve got a tricky little number in Georgia to finish off, and we definitely won’t overlook them, but it is nice to be in control of the group.”
Anscombe went on for an injured Dan Biggar after just 12 minutes in Lyon, and he promptly took charge, kicking six penalties, a drop-goal and conversion.
His 23-point haul equalled Biggar’s record for most points by a Wales player in a World Cup match, although the 32-year-old would have set a new mark had he not missed a straightforward conversion following captain Jac Morgan’s late try.
“‘Biggsy’ reminded me that apparently the last kick was to beat his record, so I am hacked off I have only tied that,” Anscombe added.
“Dan is a great man and we get along so well, but he has given me a bit of stick about that!”
Biggar looks likely to miss the Georgia game because of a strained pectoral muscle, but there are no suggestions at this stage that he could be doubtful for a potential World Cup last-eight clash against Argentina in Marseille seven days later.
“We know how important Dan is for the group, particularly on and off the field with the energy he brings,” Anscombe said.
“It was just really important when I went on that I brought some control and steadied the ship like he does so well.
“We always talk about nailing our roles, and all I was thinking about was making sure I was accurate and bringing some control.
“What was great was that we kept the scoreboard ticking. We have to give a lot of credit to our forwards. We squeezed them at set-piece time, took the points on offer and kept the scoreboard ticking off the back of that.
“I felt like I was building quite nicely in the summer (training) camps, and then I broke my hand. I thought at one point it was my World Cup done.
“I owe a lot of thanks to the team behind the scenes here. The medical team did a fantastic job to get me back on the field, and the coaching staff backed me without much game-time.
“There is still so much to work on from a personal perspective, but it was so nice to spend some time in the big arena.”