"Talk to the guys who did their part," he said. "They are the ones who put us in the position to win."
This was a win that could be traced to the offensive efforts of Ian Kinsler (two doubles, two runs scored and an RBI); Miguel Cabrera and Victor Martinez, who drove in two runs apiece; and some impressive defense that included left fielder J.D. Martinez's sliding grab of a Yoenis Cespedes sinking line drive to end the fifth with runners on first and third.
It's also true that Nathan is in the position he is in because the Tigers have been on a three-plus-season search for that lights-out closer that they think can get them that final leg of a World Series championship journey after winning the last three American League Central titles but coming up short each time in October.
There's no complaint so far. The Tigers are sitting atop the AL Central, 4 1/2 games in front of the Chicago White Sox. It, however, has not been all smooth sailing in the late innings.
Now, the Tigers aren't the only AL hopeful that has bullpen questions to answer. The two other division leaders -- Oakland in the AL West and Toronto in the AL East -- have late-inning concerns, too.
Oakland traded for Jim Johnson, who led the AL in saves with Baltimore in 2012 (51) and 2013 (50), in the offseason, but 10 days into the season he was removed from the closer's role. Oh, the A's 2.93 bullpen ERA ranks second in the AL, but their 9-for-18 save success ratio is tied with Houston for the worst in the big leagues.
Only Houston (4.93 going into Thursday night) had a higher bullpen ERA among big league teams than Toronto (4.87), which ranks just behind the Tigers (4.48) among AL teams.
And the Blue Jays have tried four relievers in the save situations, although Casey Janssen went into Thursday night with a team-best eight saves in eight chances since coming off the disabled list May 12.
The Tigers, however, were the team that made the impact move in the offseason, feeling Nathan was as good of a late-inning insurance as they could find.
And he knows it.
"Why would I come here?" Nathan asked when his signing was announced in the offseason. "I think the question is, why wouldn't I? This team is ready to win. They're ready to win now. ... It's not just about getting to the postseason. For me, it's about getting to the big one."
He has, after all, been to the postseason five times in his career, but his team has been eliminated in the first round each time -- San Francisco in the NL Division Series in 2003; Minnesota in the AL Division Series in 2004, 2006 and 2009; and Texas in the Wild Card showdown with Baltimore in 2012.
So when Nathan hits a rough spot in the regular-season road, it shouldn't be surprising that he's disappointed.
Yes, he came away with the save on Wednesday afternoon, but after giving up the walk-off, three-run home run to A's third baseman Josh Donaldson in Tuesday night's 3-1 loss, Nathan gave up two runs and had two men on base before he finally got pinch-hitter Jed Lowrie on a game-ending groundout.
It was his third appearance in three games, during a span of less than 48 hours, but he had thrown a total of only 19 pitches in earning the save on Tuesday (13 pitches) and absorbing the loss on Wednesday (six pitches).
Part of the free-agent lure of Nathan was that he has a legacy as a closer, which means he has dealt with the ups and downs and shouldn't panic.
"He has been one of the best closers in the game," first-year Tigers manager Brad Ausmus said.
That, however, doesn't mean that every day is going to be a walk in the park. Yes, Nathan does have 13 saves this season, which meant going into Thursday night's games he was tied with Fernando Rodney of the Mariners for the third spot among AL closers.
He also has four blown saves 50 games into the season, which is one more than he had in each of the last three seasons. And his 5.23 ERA. Tommy Hunter of Baltimore (6.06) is the only pitcher among the 19 in the big leagues with at least 10 saves who has a higher ERA.
With a reliever, however, those numbers can take a hit in a hurry because they have such a limited workload. Nathan had a 3.66 ERA after earning the save in the Tigers' 6-5 Tuesday win against the A's, but two days, four runs and three outs later his 2014 ERA is nearly double the 2.76 mark he compiled in the 13 previous years combined.
"With a guy who has been through it, like Joe, he can deal with these situations," said Ausmus, a former catcher.
That's what the Tigers were counting on when they signed Nathan in the offseason.
And it's what Nathan expects to do.