And Webb has wasted no time in calling for a reaction to the squad's disappointing season when they return from their summer break - including a tilt at the Challenge Cup.
"We're bitterly disappointed finishing eighth in the league," he said.
"That's not what the Ospreys stand for. We're used to winning titles and competing high in European competitions.
"We're going to put a statement out there, we want to get out of our group and go on and try to win that competition (the Challenge Cup) next season, we're renowned for winning trophies in this club."
Dan Biggar's try had given the home side an early lead before Paddy Jackson and Rory Best put the Irish province ahead.
Josh Matavesi pulled the hosts level briefly but Andrew Trimble's try sent Ulster into the break 21-14 ahead.
And the visitors maintained their lead for the rest of the match as Chris Henry, Stuart Olding and Franco van der Merwe all dotted down for Ulster, with Tom Grabham's double proving to be merely consolation.
"There are some tough teams there, but we've unearthed some good young talent and I think those boys will be ready to compete in that competition," Webb added.
"It is a massive hit to take but we've got to try to use this year in how we manage the whole squad.
"We're under no illusion we've got to improve as a whole."
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