The Scotstoun side take on Leicester Tigers in their opening Champions Cup Pool One match on Friday.
"It's a reality that we've never got to the quarter-finals as a club," said Townsend.
"We should have, given the rugby we've played - especially the last few seasons."
This time, the Pro12 side have been grouped with last season's runners-up Racing 92 as well as former champions of Europe; Munster and Leicester.
"We believe that we've not reached our potential and this year is another chance for us to do better," added Townsend, who will take over as Scotland head coach in the summer.
"We've shown not just in one-off games but in a few games how well we can play at that level," he said.
"It's very difficult - you're playing the best teams in Europe and the last two seasons we've won three of the six games. We need to win more than that."
Leicester, champions in 2001 and 2002, reached the semi-finals last season, losing to Racing 92.
"We're playing a famous club with an excellent reputation," said Townsend.
"They are a very well organised, physical team. That's always been in the Leicester DNA. Excellent set-piece, excellent line-out drive.
"In recent years they have certainly moved the ball more and they have signed some great attacking players. Telusa Veainu at full-back scored the try of the season last week.
"Matt Toomua was brought in to improve that attacking shape, to get a second receiver. He's played at 10 and 12 for Australia.
"We'll have our work cut out to look after these guys and we'll have to play really well to get in behind them."
Townsend rested several key squad members for last weekend's league win at Zebre, with only six players retained in the starting XV.
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Full-back Stuart Hogg is among those returning to action, having signed a new two-year deal this week.
"He's a great player and he's really developed off the field as well," explained Townsend. "He's one of our leaders. He cares a lot about the team and he loves playing.
"It's a good message to the rest of the players. We have a few that will be out of contract and discussions have already started.
"Dave Rennie [Townsend's appointed successor] is on board with the conversations we are having about who to retain and that's great."
Head coach Gregor Townsend admits Glasgow Warriors should have reached the quarter-final stage of Europe's top competition by now.