But with their destiny still firmly in their own hands the New Zealander has challenged the Irish region to make amends when the competition returns in January.
A 17th minute try from Gerrit-Jan van Velze, converted by Steve Myler to add to his earlier penalty, gave the English side a 10-0 lead, and despite three Paddy Jackson penalties the hosts were unable to claw back the deficit.
And it doesn't get any easier for Ulster, who face Leinster in the RaboDirect PRO12 on Friday, but Anscombe is confident his side can get back to winning ways.
"It's sad because it's our first loss but we got beaten by a better team," Anscombe said. "We're still a good team and we'll bounce back.
"It happens and you've got to acknowledge it and respect it as they did well and deserved their victory. We've got to go back and look at what we need to do better.
"Our execution was poor and we suffered from it. They got 10 points up in the first 18 minutes.
"We held them out well but I think we created enough opportunities to score points and we weren't patient enough and didn't have enough composure at crucial times.
"We tried to force it and they brought a little more passion than us to start with. Their physicality at the start got them going.
"We weren't complacent but we were a little more passive early on and we created enough opportunities but we just weren't composed enough at crucial times and we didn't take our points when we had opportunities.
"Our destiny is still in our own hands.
"We're not relying on other teams to see how it goes, if we win our last two games we'll qualify. Not every team has that opportunity - we have and we need to take
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