Bradley's side were punished by 20 points from the boot of Ian Keatley - going down 30-3 at Musgrave Park after leading through a Piers Francis penalty.
The defeat left the Gunners ninth in the RaboDirect PRO12 table with four wins and ten defeats, just four points above Newport Gwent Dragons in 11th.
But after finishing second-bottom with just six league wins and a draw to their name last season, Bradley believes there are still reasons to be optimistic.
"We didn't really threaten a whole lot in that match. It was only 6-3 at half-time but, by then, Munster had begun to establish themselves," Bradley told the Scotsman.
"We had Munster under a bit of pressure in the first 20 minutes but that was mainly because they were conceding penalties.
"There are still eight games left and we will see how we finish.
"We have been competitive. We have won four and been beaten by a score in five. The game got away from us and so too did a couple more. Compared to last year when we were pretty poor in this competition I feel we can be better."
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