With officials calling the game closely, the Giants' defense gave up too many penalties for Coughlin's liking.
"That's the charge the officials have been given," Coughlin said during his conference call with reporters after his defense was called for 10 penalties. It was the third straight preseason game where the Giants were flagged at least 10 times.
"We have to clean up the hands to the face penalties. No matter how you look at it, that's a foul. Once an official sees that, it's a penalty. There are illegal contact penalties where there was no disruption in the route. Contact happens when one turns in one direction and the other was a little behind.
Added Coughlin: "We're still trying to understand and clean it up. Quite frankly, it's a concern if the officials are going to continue calling it into the regular season. We must do something about this to have a chance to compete.
"If you're going to win at this level, you have to do a great job of reducing penalties. It is a true concern, because we're down to one preseason game. Officials, coaches and players all have to see things the same way."
The Giants' first-string defense was called three times for an illegal use of hands, twice for defensive holding and once for an illegal use of hands.
Before the preseason began, the NFL sent officials to training camps to inform teams that they would be stricter with defensive calls. The Giants' first four preseason games are proof that the league is sticking to their plan.
"Some of these fouls, I don't think are anything more than incidental things," Coughlin said. "We want that area to be cleaned up and want it now. The hands to the face calls especially. They have to make adjustments to their games."
The Giants finish off the preseason Thursday night with a home game against the New England Patriots.
Coughlin indicated that he will probably play some of his starters, including quarterback Eli Manning, for at least a few plays during the game against the Patriots, mainly because the Giants don't open the season until the following Monday night against the Detroit Lions.
However, the Giants appear to be missing a key part of their newly formed offensive line.
Guard Geoff Schwartz, signed in the offseason as a free agent from Kansas City, suffered a dislocated toe during the win over the Jets. Schwartz is scheduled to see a foot specialist Monday to determine the extent of the injury.
If Schwartz needs surgery to repair the joint, he will be lost for the season.
"The negatives from the game were the injuries," Coughlin said. "Rex (Ryan) and I talked about it before the game. We said, 'Let's have a heck of a game, but let's keep everyone healthy. When that doesn't happen, it's disappointing. Geoff's possibly going to be lost for a long while."
Coughlin also indicated that the shoulder injury suffered by receiver Marcus Harris was serious. Harris, who appeared to be headed toward a spot on the Giants' final 53-man roster, will also miss a lot of time.
Harris had led the Giants with nine receptions in the preseason prior to his injury.
"Losing two people for some length of time is not what the preseason is all about," Coughlin said.
The Giants also had defensive tackle Markus Kuhn and cornerback Zack Bowman leave the game Friday night with injuries. Coughlin said that those two injuries weren't as serious as the ones suffered by Schwartz and Harris.
NOTES: CB Prince Amukamara, who did not play Friday night due to a groin injury, ran at the Giants' practice facility on Saturday and worked out with the team's trainers. Coughlin said that he expected the starting corner to return to practice this week. ... First-round draft pick Odell Beckham, Jr. also had work done on his hamstring Saturday, but his status remains in question. Coughlin did not know Beckham's availability for practice this week. ... RB Peyton Hillis will test his ankle and foot to see if he can return. ... LB Jon Beason, still on the team's physically unable to perform list due to a broken foot, also might do some work this week. ... WR Corey Washington, who caught a touchdown pass for his fourth straight game in the preseason, continues to make a case for making the team's final roster. "Any time you make plays in a superb fashion, you get noticed," said Coughlin of Washington, who caught a 31-yard TD pass from Ryan Nassib late in Friday night's game. "He's been a big part of what we've done in the fourth quarter. He will also go up and get the ball. That's very noticeable."