The fine was first reported by ESPN NFL Insider Adam Schefter.
The first foul happened when Adams stuck out his leg and tripped Giants Pro Bowl defensive end Justin Tuck in the first half of Sunday night's game, causing Tuck to suffer an injury to his left shoulder. It knocked him out of the nationally televised contest.
Adams was penalized for tripping on the play, but that didn't stop Tuck from calling the kick a "bush" move.
"It's something he always does and he gets away with it and he continues to do it," Tuck said.
The second foul happened in the fourth quarter when Adams kicked Giants lineman Osi Umenyiora.
Adams said earlier this week that he didn't think he caused Tuck's injury.
"A shoulder injury?" Adams said. "From a supposed kick? Tell him to stay up. It ain't my fault."
On Wednesday, Tuck got his turn to respond.
"Normally, people go to the Pro Bowl for blocking people, not tripping people. So maybe he should keep his feet on the ground," Tuck said. "We're not going to get into a war of words here, we are going to let it be what it is, and I'll see Flozell when we play them again."
The rematch is Dec. 6 at Giants Stadium.
Adams has been fined two straight games. He was fined $5,000 for an unnecessary roughness penalty against Tampa Bay in the opener, which Adams said he wants to appeal.
Information from The Associated Press was used in this report.