Last season, the Flames were a No. 1 seed when they were eliminated in the first round by the Colorado Avalanche.
Calgary has reached the second round of the Stanley Cup Playoffs once since 2004. That was in 2015, Gaudreau's first full season, which ended with a second-round loss to the Anaheim Ducks after a first-round win against the Vancouver Canucks.
"It's obviously something that, with the main core there that we've had, we've kind of struggled to get past the first, second round in previous years," the 27-year-old said. "It's a hard league to play in. It's hard to play in the playoffs.
"I don't think anyone's very happy with the way the season's ended. Only thing we can do is take accounts of ourselves, take a look in the mirror, have a real good offseason -- whatever kind of offseason we're having now -- work in the gym, come prepared back to Calgary, and hopefully we have the remainder of the guys that we had this season there next season because I do think we had a really solid team this year."
The Flames also have to decide if Geoff Ward will return as coach. He was 24-15-3 after replacing Bill Peters on Nov. 29.
The NHL has not announced when next season will begin.
"Sure, I'd like to be back," Ward said. "I thought we made a big step. I thought we were moving in the direction exactly where we need to be moving. They're a real tight group. Absolutely I'd like to be back. Now, as anything this time of year, the powers that be have to sit down and evaluate and make a decision and that's what everybody goes with. We'll see how the next little bit unfolds."
Calgary has had four coaches in the past five seasons, including Bob Hartley and Glen Gulutzan.
"I think Geoff and the staff did a good job," Treliving said. "Now we have to sit back here as all of us and analyze what took place, the good, the bad, the indifferent, where we can get better and how we best want to move forward.
"I don't think you have success churning people over all the time. You need stability. That's certainly not been the plan here in terms of the coaching position but we've gone through what we've gone through. Now we have to remove ourselves a little bit from the situation, take a deep breath to let all the emotional stuff drain out, and make your decision."
Gaudreau, who has two years remaining on a six-year contract with an average annual value of $6.75 million, has 445 points (151 goals, 294 assists) in 464 regular-season games, and 19 points (eight goals, 11 assists) in 30 postseason games.
He scored seven points (four goals, three assists) in 10 games this postseason, one at even strength.
"When you're a top player in the organization or top player in the League, with that comes responsibility, and when the team does well you're going to get all the praises and when the team doesn't do well you're going to take more than your fair share of the bullets. That's pro sports," Treliving said.
"This guy, he wants to win. He wants to win as badly as anybody does. I really enjoy my relationship with John. He wants to win here in Calgary. I think even his game took some steps. Now, at the end of the day, we didn't achieve what we wanted to achieve. We're all open to criticism. That's the way of the world. If that's going to bother you, then you're probably in the wrong line of work, but I have the utmost respect for John. I know he really enjoys it here."
