Slauson will appeal the fine, a league source told ESPN NFL Insider Adam Schefter.
Cushing tore his ACL on the play and was placed on season-ending injured reserve earlier this week.
Slauson had not been informed of the fine when he was at his locker earlier Thursday.
"I've heard (from my coaches) that it was a clean block, that's all I know," Slauson said. "If the league wants to tell me differently ... I hope I don't get fined. If I happen to get something, I'll deal with it then."
Replays showed Slauson diving at Cushing's legs. Jets coach Rex Ryan said Wednesday that he thought it was a clean hit. Asked if there was an illegal aspect to the hit, Ryan said, "No. I think that's just one of those unfortunate things."
A peel-back block is deemed to be illegal if initiated to an opponent's back or the side, according to the NFL rulebook.
Earlier Thursday, Houston defensive coordinator Wade Phillips called the hit unnecessary.
"Whether it was legal or not, all that stuff -- I think it's just unnecessary to hit a defensive player when he can't see you," Phillips said.
Slauson was not penalized on the play. Phillips said if he'd hit Cushing in his head, he would've drawn a flag.
"If a guy's coming in front of me and cuts me, he can see that and yeah, they can get away with that," Phillips said. "But when they don't see you, I think the league needs to look at something like that."
"I know the intent of Matt Slauson was not to injure Brian Cushing, without question," Ryan said. "We wouldn't try to injure anybody, but a great player like Brian, it's really an unfortunate thing. It's obviously in their (the league's) hands, but I know the intent of our player, though."
Added Texans left tackle Duane Brown: "The way we cut, it's always going upfield. The way he (Cushing) got cut, the guy (Slauson) was actually coming back toward the play. He was facing the running back, coming back toward the line of scrimmage, which I don't think is legal. We don't coach that at all. We don't go out and execute that kind of cut block."
Brown said cut-blocking is "encouraged" in Houston's offensive scheme, but added, "You have to be careful."
Phillips praised the league's efforts to monitor illegal hits.
"I think the league is trying to do all the right things, they always have," Phillips said. "When these cases come up, they look at them. I think the league will look at it."
Information from ESPN NFL Insider Adam Schefter and The Associated Press was used in this report.