However, he acknowledged that the quarter-final loss to Toulon represented a missed opportunity, particularly with the chance of securing a home semi-final slipping away.
Speaking to the media after the match, Smith said: "We created the expectation. People think that we can win this competition, and that is a big mind shift.
"Maybe that is the motivation we take from this, is to believe we can make that next step.
"I'm not saying we didn't show that today, but the fact that we played at home and everybody's coming out here and everybody's excited about that, that little expectation, it comes into the changing room."
Despite the upcoming departures and with only Ruwald van der Merwe confirmed as a new arrival, Smith is adamant his squad will remain competitive.
"We've lost big players before," he said.
"I think obviously Jack, Huw, Johnny and Adam, they've contributed massively but the understudies are there. The next guys are there.
"I'm absolutely not concerned. This is a solid club. We believe in significance, not in success.
"We will continue to produce a very good product, regardless of some of the results. So, who comes and goes, who are on the ship or on the train for a short part, but the train is not going to stop. It's going to keep going."
The Warriors head coach also admitted his side were surprised by Toulon's physicality and praised the French club's performance.
"I'll take my hat off to Toulon," he said.
"Their physicality was way better than we expected from the preparation that we've done on them. They obviously had a big emphasis on that part of it, which we're proud of, because we'd like to challenge other teams physically.
"And I thought they brought it from a set-piece perspective, and definitely on the defensive side of things. So well done to them. I hope they progress further, because I thought they showed some good endeavour coming here as underdogs."
A try from Juan Ignacio Brex ultimately proved decisive in Toulon's 22-19 victory, despite a late surge from Glasgow as they piled on pressure in the closing stages.
There were opportunities for a drop-goal late on, but Smith defended the decision not to take a shot at goal.
"I would rather have preferred a penalty and then make the decision - we weren't close enough," he said.
"To put it on to one guy, drop it or miss it, all expectation goes out the door through a try.
"We were building phases there. Maybe a penalty and then a decision after that to go into extra time would have been made but unfortunately they weren't that quick."
Smith also confirmed that Adam Hastings and Max Williamson will miss the upcoming tour to South Africa due to concussion and a knee injury, respectively.
Williamson, who withdrew late from the bench, could be sidelined for up to six weeks, further weakening Glasgow's second-row options.
The squad is now limited to Scotland international Alex Samuel and Jare Oguntibeju as recognised locks for the two-match tour, with Euan Ferrie providing additional cover.
"We are challenged there. Alex Craig, Gregor Brown, Scott Cummings and Max Williamson not available for this game was tough, but I thought Fez [Ferrie] and Jare and Alex did a great job for us to play a world-class team like we've done and just fell shy of winning and beating them."