The day after, Danilo Gallinari looked like the worst hangover you’ve ever had. And for all the understandable satisfaction the Hawks and their fans have taken in this loud and stunningly robust season, the hangdog Italian was having little of it.

Gallinari and Lou Williams are the only Hawks born in that long-ago decade of the 1980s, such is the callowness of this bunch. During parting interviews Sunday, having been too worked up to sleep since his team was eliminated with extreme prejudice by Milwaukee the night before, Gallinari took a little bit of the grumpy-old-guy route.

“I don’t know if it’s because of my age (32, the old coot), maybe I have some more motivations to not be happy right now,” he said. “These kind of seasons don’t happen every year. I think you guys can see what happened to (Phoenix’s) Chris Paul. It took him 16 years not even to win it but to just have the chance to play in the (NBA Finals). Everybody needs to understand when you have the chance to do something special like we did this year, you got to use it and take advantage of it.

“I think we had a chance. If I think we didn’t have a chance, I wouldn’t be this mad – or disappointed – right now. I thought we had a chance, and we didn’t use it.”

Someone has to be the Randy Realist in the room and remind these playoff newbies that what they just did was in the next county over from the norm. And that to take it for granted that they will be knocking on the door to the NBA Finals again and again would be foolish arrogance. Sport laughs at assumption and regularly gives expectation a fierce wedgie. And make no mistake, the Hawks have left behind the darling-overachieving stage and will be asked next season to win like it is in their nature.

Maybe these Hawks can be something like the 1991 Braves, the worst-to-first team that launched a long, standing reservation to the postseason and even one – sigh, just one – world title. Maybe we are just on the cusp of a Hawks dynasty, but remember that “maybe not” also is no worse than a 2-to-1 bet. Teams like Milwaukee and Brooklyn are not going to take off the rest of the 2020s. And should Ben Simmons learn that shooting a basketball is part of the job description, Philadelphia might even have something to say. These Hawks are not growing up in a hothouse. It is a tough and demanding world out there in their league.

Toward that end it would be nice if the Hawks can shore up a few things before training camp.

That starts at the top with Nate McMillan, who should no more be considered an interim head coach than De Niro be deemed a stand-in. “He told us to believe, and he backed it up,” Solomon Hill said of his coach. Now, we gotta believe that the Hawks will quickly make the arrangement with McMillan more lasting and that some other team doesn’t poach him after his striking makeover this postseason.

There persists the question of what part John Collins will play in the Hawks’ continued growth. “Obviously we’re going to have to come to a decision very soon. Hopefully it will be the best one for me and the one that keeps me here,” he said Sunday.

Having reportedly turned down a $90 million extension while looking for a so-called max contract, Collins may have to recalculate his worth. Or, if there is a team out there that will go to the max for him, he may have to scout out some trustworthy movers. Understandable if the Hawks choose not to over-pay for him.

And GM Travis Schlenk can take no long naps, either. His roster, while promising, is not complete. The Hawks still need to import or develop another consistent creator on offense for when Trae Young isn’t quite himself. A little defensive muscle wouldn’t hurt, either.

Then there is the matter of young players on hand growing some competitive calluses, learning from this run to the conference final and being steeled by the experience.

Here we defer to the wisdom of Solomon. That’s the aforementioned and well-seasoned Solomon Hill, the 30-year-old playing for his fifth team. He didn’t play a lot minutes for the Hawks, but what time he logged, he tried to make intense.

“We need some edge,” Hill said Sunday. “It’s one thing to come from me, but we have to have somebody out there that’s clocking big minutes that has an edge, some grit to them.”

“This can’t be easy,” he continued. “Last night was the opportunity to play the hardest game that anybody in that locker room has ever played in their life. ... Last night is when you needed dogs. It’s tough when you’ve never been there, but we need that grit. We need somebody other than (Clint Capela) to anchor the defense and to be vocal.”

Milwaukee had that at the end, and the Hawks didn’t – that simple, Hill said. The Bucks’ past had prepared them for the night, even without their star back from a knee injury.

“They attacked the paint, they were forceful,” Hill said. “Whether it was Bobby Portis, Jrue Holiday, P.J. Tucker, they brought a certain edge to the game that only comes when you’ve been in the playoffs and you’ve lost and been ridiculed.”

No ridicule fits the Hawks at this stage, of course. This is a time to appreciate a team that climbed higher than its ladder should have allowed.

But also a time, the older hands will confirm, to let some real, deep disappointment work for you, a bitter investment in the future.