Houston Texans defensive end Antonio Smith's appeal of his pending NFL suspension was denied, a source told FOX Sports Friday.

Smith, who swung a helmet at Miami Dolphins guard Richie Incognito last Saturday, was appealing a ban for the team's final two preseason games and regular-season opener.

FOX Sports NFL insider Jay Glazer obtained video footage for FOX Football Daily (6 p.m. ET, FOX Sports 1) that showed Smith ripping off Incognito's helmet and swinging it toward his face during last Saturday's preseason game. The blow glanced off Incognito's shoulder.

Smith and Incognito have tussled in previous matchups. Smith told FOX 26 in Houston on Tuesday that he was "disappointed in myself I was able to let (Incognito) get to me in the way that he did . . . I just swung the helmet out of frustration."

Smith can attend team meetings before the next two preseason games but is barred from practicing, and playing Sunday against New Orleans or Aug. 29 against Dallas. He may not participate in any team activities until reinstatement on Sept. 10, the day after Houston's regular-season opener against San Diego.

One of the Texans' top defensive players, Smith will forfeit about $353,000 for the games missed. That translates into one-seventeenth of his $6 million base salary in 2013.

A flag wasn't thrown on the play that drew such a stiff punishment from the league office. The NFL acknowledged Wednesday that Smith should have gotten penalized for unnecessary roughness and ejected for using his helmet as a weapon.

League spokesman Michael Signora pointed to Rule 12, Section 2, Article 16 of the NFL rulebook that states, "A player may not use a helmet that is no longer worn by anyone as a weapon to strike, swing at, or throw at an opponent. Penalty for illegal use of a helmet as a weapon (is) loss of 15 yards and automatic disqualification. If the foul is by the defense, it is also an automatic first down."

Incognito, who has tried to shed the label of being a "dirty" player from earlier in his nine-year NFL career, addressed the subject Tuesday with Dolphins media.

"Football's an intense game," Incognito said. "It's played with a lot of passion. Blood runs hot. I've been there. I'm no choir boy. People lost their cool. Just thank God no one got hurt."