Andrew Trimble opened the scoring before Paul Marshall crossed twice, with Paddy Jackson adding 19 points with the boot on what would appear to have been a comfortable night for Ulster.
But, despite coming away with five points, Bowe admitted there was still plenty of work to do, with Castres' two tries making it a nervy first half for the hosts.
"We're delighted to get all the points but there are areas we are going to have to work on," said Bowe.
"After Paul's first try we fell off a little bit, which is similar to what we did against Connacht and we need to be more wary about that as the season progresses."
"It wasn't as clinical as it could have been and you won't always get away with that."
With Ulster now unbeaten in six so far this season Mark Anscombe's men are looking like a formidable force, and Marshall believes every European win breeds confidence they can take into the RaboDirect PRO12.
"If the team goes well it helps everybody and if you come into a game unbeaten as we did it boosts confidence," he said.
"With Mark rotating the squad everybody's fresh, everybody's keen and there's a real competition in the squad which will hopefully keep us active in both the league and the Heineken Cup."
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