That was never more evident than what transpired in the D-backs clubhouse following their Game 5 elimination loss to the Brewers in the 2011 National League Division Series.
Putz was on the mound when the Brewers scored the winning run in the 10th, ending what to that point had been a storybook season. When the media was allowed in the clubhouse 10 minutes later, Putz was standing in front of his locker, where he patiently answered question after question.
"It was definitely unfortunate the way it ended," Putz said. "But that's the game. It is what it is."
Putz learned the lesson of being accountable during his time at the University of Michigan. Bruce Madej, who worked in the athletic department's sports information department, passed along a story about how he instructed Chris Webber to immediately face the media following his mistakenly-called timeout in the 1993 NCAA Men's Basketball National Championship game.
"That always stuck with me," Putz said.
And it made an impression on his teammates.
"Obviously it was disappointing for him, and maybe other people would have blown off talking to the media, but he stood in front of his locker and talked to everyone who came to him," rookie reliever Bryan Shaw said. "That's just the way he is."
To be a successful closer requires that he be able to bounce back quickly from a less-than-perfect outing, and Putz embraces that mentality.
Even with no game the next day to worry about, Putz knew that he couldn't let the loss linger.
"Literally when I got home I had let it go," Putz said. "That's just the way I was taught. You can't afford to hang onto it, good or bad."
Putz was signed to a two-year contract prior to the 2011 season as part of GM Kevin Towers' desire to reshape what had been one of the worst bullpens in Major League history.
On the field, Putz led the way by saving 45 games in 49 chances, but behind the scenes he was also an important part of the team.
"There's a lot more to J.J. than you guys actually see," D-backs manager Kirk Gibson said. "What he does on the mound is obvious. He's a great competitor. He's very dedicated to what he does and we're very fortunate to have him down there in the bullpen."
Part of what Putz did last year was lead young pitchers like Shaw, David Hernandez and Joe Paterson.
"Seeing him do it and the way he does it, getting mentally focused, that's one way I consider he leads by example," Shaw said. "He helped me out a lot when I first got called up."
As young pitchers Trevor Bauer and Tyler Skaggs will soon find out, Putz is a good resource.
"I know that when I was younger, I would lean on the older guys in the 'pen," Putz said. "Just conversations about certain hitters and this and that. I look forward to talking with Skaggs and Bauer, just to see what's going through their heads."
Putz also likes to keep his teammates loose, and if there's bubblegum stuck to a player's hat or a practical joke happening, chances are he's right in the middle of it.
With his undying loyalty to the U-M, Putz and Michigan State alum Gibson have their share of trash talking back and forth.
Last season, Putz was at the center of a practical joke on Gibson, in which the players all wore ties for a chartered flight that had pictures of Gibson in a 1989 commercial. Afterwards, Gibson playfully vowed revenge.
He is still waiting for the right moment to exact it.
"I'll pick a good opportunity," Gibson said. "I'll get him. If he keeps getting guys out, he can prank me all he wants."
Steve Gilbert is a reporter for MLB.com. Read his blog, Inside the D-backs, and follow him on Twitter @SteveGilbertMLB. This story was not subject to the approval of Major League Baseball or its clubs.