"Football is an intense game," Incognito said before taking questions from reporters. "It's played with a lot of passion. Blood runs hot. I've been there. I'm no choir boy. People lost their cool and I just thank God nobody got hurt."
Smith ripped Incognito's helmet off after a Dolphins pass play in the first half of Houston's 24-17 victory at Reliant Stadium and swung it at Incognito. Television replays don't clearly indicate whether the helmet made contact with Incognito's face and he declined to provide the answer.
No penalty was called on the play.
When asked how he kept his cool after the incident, Incognito replied: "You're faced with those situations all the time. It's been a work in progress for me. It's something I've been working on for many years now. I have too much respect for my teammates and too much respect for the hard work that we put in to retaliate and affect this team negatively."
Incognito long has had a reputation for his aggressiveness. He was named in a 2009 Sports Illustrated poll as the dirtiest player in the NFL while he was a member of the St. Louis Rams and last November he finished second in a similar poll conducted by The Sporting News.
The incident Saturday night wasn't the first involving Incognito and Smith.
Smith was fined $11,000, after appealing an original fine of $21,000, for kicking Incognito during the 2012 regular season opener at Reliant Stadium. Smith later said that Incognito had deliberately tried to twist his ankle while holding his legs. Incognito did not incur a fine for that play.
Incognito was asked when his problems with Smith started, and he declined to answer, saying he was focused on the Dolphins' upcoming preseason game against Tampa Bay Saturday night.
Dolphins coach Joe Philbin also declined to get into specifics about the incident Saturday night.
"I certainly don't coach the Houston Texans, so I'm not going to comment on their players," Philbin said. "It's important that our players play the right way, do things the right way on and off the field. That was Saturday night; today is Tuesday afternoon. I'm focused on the Tampa Bay Buccaneers."
When he was asked whether Incognito handled the situation Saturday night the right way, Philbin replied: "It's not really for me to judge. It's on film People can come to their own conclusions."
Center Mike Pouncey took the same approach when asked about the Incognito-Smith incident.
"We're moving forward on it," Pouncey said. "The league office is going to do a good job of handling it. Right now we're just worried about this game coming up on Saturday."