Kirk shot into contention for earning one of the three wildcard picks for the USA's bid to win back the prestigious team trophy at Gleneagles starting September 26, after he won the Deutsche Bank Championship on Monday.
However, the new FedEx Cup play-off leader was bypassed in favour of Keegan Bradley, Webb Simpson and Hunter Mahan.
"It was a fine conversation, he [Watson] was pretty straight to the point. He just said 'congratulations on your great play but we are going to go in another direction'," Kirk said.
"He started to explain his reasoning. I wasn't rude or anything, but if you're not the one getting picked, the reasoning doesn't really matter a whole lot.
"I told him not to worry about it, you've got to do what you've got to do.
"I just won the biggest tournament of my career, it' going to take a lot more than this to put me in a bad mood."
Kirk echoed the thoughts of world number one Rory McIlroy, claiming the condition of the greens will be key for this week's BMW Championship at Cherry Hills Country Club.
"I really have no clue what kind of scores to expect from this week," the 29-year-old said.
"I've never been a good judge of that going into new courses. I think it all depends on how firm the greens are.
"If they get the greens really firm and they put some tough pin placements out there, with how much slope there is in these greens that will definitely be the defence.
"If the greens are receptive you will see some pretty low scores."