TAMPA, Fla. -- New York Rangers coach Gerard Gallant sat inside a conference room at Amalie Arena, discussing how his team's surprising Stanley Cup playoffs run ended in Game 6 of the Eastern Conference finals. On the other side of a wall sat coach Jon Cooper, surrounded by Tampa Bay Lightning conference championship hats and riding a much different vibe.

"Gerard Gallant is going to be sitting here in not too long," Cooper said, pointing to the victors' podium.

It could have happened this week. The Rangers held a 2-0 series lead over Tampa Bay. Goalie Igor Shesterkin had carried his superior play from their seven-game Round 2 victory against the Carolina Hurricanes into the conference finals. He would make 49 saves in Game 3, but couldn't stop the biggest shot of the contest: Ondrej Palat's goal with 42 seconds remaining in regulation, brilliantly set up by Nikita Kucherov, to give the Lightning new life in the series.

This would be a common theme for the next three games. They couldn't find that goal to tie up Game 4 after Pat Maroon's tally early in the first, or that second goal in Game 5 that would have prevented more Palat heroics in the last two minutes of regulation, or that tying goal in Game 6 to earn overtime after Steven Stamkos answered their power-play tally in the third period.

"We played well. We battled hard. We had a chance to win all those games but they found a way to get that goal at the right time," Gallant said.

His Tampa Bay counterpart often talks about how the Lightning's crushing 2019 first-round sweep loss to the Columbus Blue Jackets was a transformative moment for his team. The Lightning have won 11 straight playoff series since then -- Cooper quoted former Jackets coach John Tortorella as saying he created "a monster" in the victory -- and learned one of their most important lessons against Columbus: Nothing is achieved unless it's earned.

"We don't care how it gets done. It just needs to get done," Stamkos said.

The Lightning had lost in the conference finals two of the previous three postseasons. Their 128-point regular season in 2018-19 was one of the best in NHL history. Everything pointed to their ascension to the Stanley Cup. Four games later, they were the laughingstock of the league.

This is one of the lessons the Rangers must learn from this Eastern Conference finals loss. The expectations that the Rangers are the "next one" are already there, from Jon Cooper's mouth to CapFriendly's pages, which reveal a Rangers team positioned well in terms of age and salary space. The hunger to get back will be there. But success can't be assumed.

Now comes the hard part.

Here are some of the lessons for the Rangers to take away from their loss to the Lightning in order to take that next step.