Anscombe's troops had won 11 successive games in the league, but fielded a weakened side ahead of crucial Heineken Cup ties in the New Year against Glasgow Warriors and Castres Olympique.
Ulster belied their under-strength status and were unfortunate to go in 10-3 adrift at the interval courtesy of a penalty try and five points from the boot of Ian Keatley.
Two tries shortly after the restart, from Simon Zebo and Peter O'Mahony, put the game beyond Ulster but Anscombe still drew on the positives - including Ali Birch's first try for the club late on.
Anscombe told the Irish Independent: "We are still in there, we are still in a healthy position in the table and we had a lot of young guys in there who got some game time in there.
"Hopefully they'll be wiser and better for it and it will benefit them in the season ahead."
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