But since their last championship in 2017, they have won one playoff round.
And the new management team of Ron Hextall and Brian Burke will have to figure out how to proceed after the Penguins unexpectedly won a division title but lost in the first round to the New York Islanders for the second time in three years, falling 5-3 in Game 6.
Crosby says he has heard the speculation about whether it's time to break up the core for years.
"I know the three of us, we want to win," he told reporters. "We’ll do whatever it takes to try to compete to do that every year."
WEDNESDAY ROUNDUP: Lightning, Islanders advance with Game 6 wins
The Penguins had to deal with the abrupt resignation of GM Jim Rutherford and struggled early before turning it around. Hextall's acquisition of Jeff Carter at the trade deadline paid off as he got nine goals down the stretch and five in the playoffs.
"Up and down the lineup, it’s a team that can definitely compete for a Stanley Cup," said Carter, who has a year left on his deal. "The hunger is still in that room and that comes from the top guys."
The Barry Trotz-coached Islanders won the final three games, even without a goal in the series from regular-season points leader Mathew Barzal. They got a strong performance from goalie Ilya Sorokin after he returned to the net in Game 4.
"They play a very structured game, a very simple game and patient game, and when they get opportunities, they capitalize on them," Carter said of the Islanders.
Penguins goalie Tristan Jarry, meanwhile, made a bad pass in losing Game 5, then yielded five goals on 24 shots in the clincher. The Penguins had three one-goal leads in the game, only to see the Islanders tie and take a two-goal lead.
"I thought when the game was 2-1, we got a huge save and that gave us momentum and we came back and got to 2-2," Trotz said. "When it was 5-3, on the Malkin breakaway, we got a huge save and that settled us right down."
Said Crosby: "There’s zero doubt in my mind that the group we have is a really good group and we had a real good opportunity here, and that’s why it stings so much."
Crucial sequence in Wild victory
— NHL on NBC Sports (@NHLonNBCSports) May 27, 2021
Coach Peter DeBoer challenged and lost, getting the explanation that Tuch didn't try to get out of the crease. That led to a delay of game penalty, and Minnesota's Kevin Fiala scored on the power play. Instead of a tie, the Golden Knights were down 2-0. The Wild won 3-0.
"Those (reviews) have gone our way before," DeBoer said. "We felt it was worth the challenge. Our PK's been excellent all year. That point of the game, we felt it was a close enough call that it was the right thing to do."
"This is why you work your ass off all season to have the record you have to host this game in your building," DeBoer said.
Lightning's Vasilevskiy shines
He also let in the first shot he faced in Game 6. The difference Wednesday: Tampa Bay's Andrei Vasilevskiy, considered a front-runner for the Vezina Trophy, stopped all 29 shots he faced for a 4-0 series-clinching victory.
"They got a great young goalie over there and we have the best right now and he showed it tonight," Lightning captain Steven Stamkos said.
Thursday's playoff games
Montreal at Toronto, 7 p.m. ET, NBCSN. Maple Leafs lead 3-1.
Carolina at Nashville, 9:30 p.m. ET, NBCSN. Hurricanes lead 3-2.
This article originally appeared on USA TODAY: NHL scores: Penguins face questions; review call costs Golden Knights