Despite Saracens having a man advantage Ulster refused to lie down and led 9-5 at half-time, only for Sarries to come firing back after the break to squeeze out a 17-15 victory.
And while disappointed to lose Bowe, who featured in all three Tests against Australia for the British & Irish Lions despite suffering a broken hand - believes Ulster can still hold their heads up high after running Saracens close.
"The whole build-up, the fact that we had Saracens; who we know are a difficult side to play against, but we felt we had the beating of them," he said.
"We were up against it. To lose one of the back three against Saracens who are pride themselves on their kicking game, it was always going to be extremely difficult for us, but I think we catered to it very well.
"We dug in as a team. We had to do it around the park and it was credit to the squad we've got and the talent we've got that this team came so close to a win, but to come so close to winning it makes it that bit more difficult.
"Hopefully there will be a lot more success here for Ulster in the coming years."