Warriors lifted the PRO12 title last year and will have the chance to make it two in a row if they can overcome Connacht in Saturday's semi-final.
Glasgow have reached five consecutive PRO12 play-offs but have failed to carry that form into the European Champions Cup.
The Scotstoun side have never made the knock-out rounds of the continental tournament and Peter says they will only get respect when they get out the pool stage.
The Scotland centre told Press Association Sport: "Last year our motivation was becoming the first Scottish team to win a title, now we want to become the first Scottish team to back a title up.
"We want to make winning trophies a habit. We want to become one of the top teams in Europe but won't achieve that just by winning the PRO12 once in a blue moon.
"I don't want people to be like, 'Remember when Glasgow won it back in 2015?'. I want to win it a few years running so folk think of it as Glasgow's era of dominance.
"We've still not cracked Europe and it's a real bugbear for all of us. We were distraught when we missed out on the quarters again this year.
"I think we've got respect in our league but in Europe? Probably not. The English and French teams still probably look at us as being 'little Glasgow'.
"But the only way we're going to get credit or respect from the top teams is to win trophies.
"If we can win the title this year, especially with everything we've had to contend with like the World Cup and a lot of injuries, then people really will sit up and take notice."