In the 2022/23 campaign, Warriors went unbeaten at home through the regular season of the URC, only losing to Munster in the quarter finals, and they also reached the final of the European Challenge Cup, where they lost to Toulon.
After such a positive start to this season on Sunday, Dobie is optimistic over Glasgow's chances of another positive year.
Speaking to the Inverness Courier, Dobie said: "I think it was massively important to start this season off with a win. We had a really strong season last year and I think we caught a few teams by surprise, but that means the expectation on this team now is higher.
"There was no better team to get a win like that against than Leinster - who have dominated the regular season of this league in recent years. We fronted up extremely well, and getting a win like that is a bit of a statement.
"We need to keep building on that momentum now, there's no point starting with such a strong win if we can't back it up. That's the next challenge for us.
"I'm extremely proud of the performance. There were a couple of moments there where the momentum got away from us, and it would have been easy for a team like Leinster to run away with it - so to dig deep shows how far we've come.
"It has been a long time since that quarter final against Munster which hurt us a lot, so it gives us that platform to build now.
"The way that the league is structured this year, it's a lot of back-to-back games, so we can build on this.
"Whether home or away we know we can put in performances, because we've got the squad and the depth to do it. We will back each other up the whole way."