Head coach Gary Kubiak said he and the Texans were "disappointed" in the decision.
"We thought we had an excellent chance to get him back the first week," Kubiak said Friday. "But like I said: I think our League's fair, and they look at everything.
Kubiak said the loss of Smith is just "challenge number one" for the club in 2013, and that the Texans will certainly encounter more challenges this autumn.
"I'm sure there will be many more throughout the course of the season," Kubiak said. "We understand it. We accept it. As a team, we've got to get ready to meet the challenge."
Smith's helmet swing violated Rule 12, Section 2, Article 16 (page 71) of the NFL Rule Book, which 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.”
As explained in a team press release from Wednesday, beginning on Saturday, August 31, Smith is suspended for Week 1 of the regular season and may not take part in any team activities. He will be reinstated on Tuesday, September 10.
In Smith's place Sunday, Kubiak said fifth-year veteran
"We’re going to rotate guys, but Timmy’s the guy right now," Kubiak said. "We’ll play a lot of people.”
Smith's teammates said they'll miss him, and remain supportive of the defensive captain.
"We stand behind Antonio one hundred percent," Joseph said. "He's a guy that makes this defense go, from a leader standpoint. Everybody rallies behind him."