During Darren Sharper's 99-yard interception return for a touchdown in the second quarter Sunday, Sanchez dived at the legs of Vilma, who was blocking on the play. Sanchez was assessed a 15-yard personal foul penalty for the hit.
Vilma took exception to the block, saying after the game the league should fine Sanchez. The league offices don't confirm fines until Friday.
"Yeah, I got a little fine for that," Sanchez said.
Sanchez said he called Vilma on Tuesday and apologized.
"I'm running down the field and I'm upset after the pick, and I said, 'Hey, dude, I don't know what I was doing," Sanchez said. "I was just trying to create a pile, just push somebody into a boundary because I don't want to be the guy on film who's quitting on the play. At the same time, I don't want to take the guy on head-on and get in trouble for putting myself in danger.
"I just told him I've got to be smarter than that."
Sanchez said the former Jets linebacker told him, "No problem at all. I understand. Good luck."
Sharper's interception was the first of four turnovers by Sanchez against the Saints, including three picks. He also had a fumble that was recovered in the end zone for a touchdown.
"The tale of that game was 14 points," he said. "We lost by 14 points. They scored 14 points when we were on offense and that's unacceptable. Those mistakes, I need to clean up."