Tuck made the comment after the Giants fell to 0-4 with a 31-7 loss to the Kansas City Chiefs.
"If anyone turns on our coach, I would be the first one to punch him in the mouth," Tuck said, according to the New York Daily News. "And put that in print. It better not happen, I know that."
Giants wide receiver Victor Cruz questioned one of Coughlin's decisions in Sunday's game. With the Giants trailing 10-7 late in the third quarter and facing fourth-and-1 at their 30, Coughlin elected to punt rather than go for a first down.
"We've got to take a risk at some point and make something happen," Cruz told reporters.
The punt was returned 89 yards for a touchdown by Dexter McCluster, giving Kansas City a 17-7 lead.
When asked about Cruz's comment on Monday, Coughlin said he was not concerned, even joking about the matter.
"I gave him a chance to say something today," Coughlin said, laughing. "I asked him if he wanted to fight?"
When asked how Cruz responded, Coughlin said, "That's between he and I, but it was in good humor. I didn't ask him what his thinking was.
"I don't understand why you guys would make so much out of something like that, but it's kind of comical. That circumstance, that quote there, you should have just realized it was frustration."
The Giants, just two years removed from winning the Super Bowl, are 0-4 for the first time since 1987 and the first time in a non-strike season since 1979.
New York lost a close game in Week 1 at Dallas (36-31) but has been blown out three weeks in a row by Denver (41-23), Carolina (38-0) and Kansas City.