Anscombe watched his side see off the Tigers 22-16 at Ravenhill before they became the first team to triumph at the Stade Yves du Manoir this season just a week later as they took control of the group ahead of December's double header with Benetton Treviso.
Ulster were on a run of six straight wins since back-to-back losses at the start of the RaboDirect PRO12 season and things were looking increasingly bright in Belfast. But deafeat at the Scarlets on Saturday night brought that run to an end as Ulster failed to get out of second gear in Llanelli.
They now have a fortnight's break before returning to league action against Edinburgh on November 22, with the home tie with Treviso next on the cards after a trip to Zebre, and Anscombe believes the time off could be just what they need.
"We have a couple of weeks off now and I think that will be a good thing," said Anscombe.
"We had a good win last week against the Blues but it wasn't a great performance and we had a pretty average one out there again against the Scarlets.
"Hopefully a few days off for the boys will refresh their batteries. Players like Nick Williams looked short of a game out there, so we need to get them back into the fold.
"The first week a good few guys will have a week off and we will get them back Monday week and go about our work and get ready for Edinburgh."
Ulster's results so far this season…
Newport Gwent Dragons (A) L 15-8
Glasgow Warriors (H) L 13-12
Connacht (A) W 18-7
Benetton Treviso (H) W 32-13
Ospreys (A) W 18-12
Leicester Tigers (H) W 22-16
Montpellier (A) W 25-8
Cardiff Blues (H) 39-21
Scarlets (A) L 17-9
Edinburgh (H) Nov 22
Zebre (A) Nov 30
Benetton Treviso (H) Dec 7
Benetton Treviso (A) Dec 14
NB Bold denotes Heineken Cup fixture