Lee left his feet when he was knocked to the ground as quarterback Russell Wilson scrambled down field.
Cowboys owner/general manager Jerry Jones said he expects the NFL to review the play and possibly issue a fine.
"I'm sure they will," Jones said. "We saw the same thing you saw. That’s certainly something we know or expect penalties and fines about. They didn’t see the helmet hit or they would have called it."
A penalty was called during the sequence of events, but not against Seattle.
Linebacker Bruce Carter was flagged for pushing Wilson out of bounds, a questionable play because replays showed the quarterback with one foot in bounds.
Tate, meanwhile, celebrated the play by crawling on his knees and then pointing to the back of his jersey.
"That’s part of the deal," Lee said. "He can celebrate all he wants. I bet you if we went head-to-head and square up he probably won’t be celebrating as much. It’s part of the deal and part of football, and hits like that happen."
Lee said he was hit in the chest and not the chin. The Cowboys' medical staff cleared Lee to return after he passed concussion tests.
Still, the hit irked the Cowboys because they thought it was questionable.
"It really pissed me off if you want to be honest," linebacker DeMarcus Ware said of the hit. "Anybody that sort of retaliates on any of the other players on defense, offense, you sort of got to take that mentality back to them. That’s part of this game. It’s a brutal game, but we didn’t do that."
Tate wasn't asked about the celebration but noted, "I was just trying to hit him a little bit and get him on the ground."
When asked if he thought he would get penalized, Tate said, "I wasn't sure. I knew that I didn't hit him in his helmet. I hit him somewhere down here (Tate pointed to his chest). But the rules change so much that you never really know. I'm happy that it wasn't (flagged)."
Coach Jason Garrett normally isn't critical of the officials, and with the league using replacement refs, he's being extra careful of his comments.
"I didn’t get a real complete explanation," Garrett said. "All the referee did was explain to me the penalty was in fact called at the end of the play on our guy on their sidelines. Again, that was a play in the ballgame but it probably had nothing to do with the outcome of this ballgame."