No team has ever failed to reach the knock-out stages as a runner-up with 22 points, but without the bonus point they still have a little bit of work to do to ensure they go into the hat for the quarter-finals.
The win temporarily took the gap between Ulster and next week's rivals, Leicester Tigers, to seven points, but the Tigers could cut the gap to two if they clinch a bonus point victory in Italy against Benetton Treviso.
"We are pleased with the win, but we are not pleased with the way we executed today. We were a bit loose. They came here with nothing to lose and they tried to get amongst it and they have got a big pack and caused us a bit of trouble," said Anscombe.
"But we didn't keep our composure and we tried to play them at the same type of rugby they brought with them. We needed some form of structure and that would have taken the game away from them.
"We had a couple of close chances to score that bonus point try, but at the end of the day it ws always going to come down to next week, so nothing has changed. We will take the win - we are five from five and you've got to be happy with that.
"They had some big boys in their pack and they took it to us up front. Their kicking game was good and we played a bit of ping-pong with them and got a good return from it, but they had nothing to lose. The results didn't really matter to them and the game got loose and lost its structure. That suited them and we allowed it to carry on. We needed to bring some composure.
"We have got to look after the ball and be more disciplined. We gave away six penalties at vital times in the first half and that allowed them to keep plugging away with three points. That kept them in the game and our discipline has been hurting us a bit in the last few weeks. We won't get away with that next week and it is something we will have to work on."