The coach reckoned the Warriors resorted to illegal 'ball-killing' tactics to snuff out his team's attacking moves - and he slated Welsh ref Hugh Watkins.
Bates said: "Rugby revolves around getting the ball quickly. My interpretation was that the ball was not coming out to us as fast we expected. The only way to stop it coming out is to cheat.
"There was persisting offending and not just in areas where you think you might be able to score.
"We need to be clear about what we constitute as interfering when the ball is downon the floor. We lost attacking opportunities because the ball was slowed down, particularly late on."
Borders skipper Paul Thomson also claimed that an unsuccessful penalty by stand-off Charlie Hore did fly between the uprights - a score that would have levelled the game.
Glagsow were also unlucky when a try was chalked off for a non-existent knock-on.
Relieved Glasgow coach Hugh Campbell said: "We were probably fortunate to come out on top. Dan Parks' kicking managed to pin Borders down in their half and made them play from deep."