"Everyone should realize where this team is," Tate said Tuesday on 710 ESPN radio in Seattle. "You are affecting way more than yourself. I feel like that was kind of a selfish move on both those guys' part.
"But it is what it is. The show must go on and that's what we're gonna do."
The Seahawks, who have the NFL's best record at 10-1, host the New Orleans Saints (9-2) on Monday night in a game that could decide home-field advantage in the NFC playoffs. Seattle is 13-0 at home over the past two seasons.
As expected, the Seahawks announced Tuesday afternoon that Thurmond had been suspended without pay for the next four games for violating the NFL's substance abuse policy. Thurmond will be eligible to return to the active roster Monday, Dec. 23, following the team's home game the day before against the Arizona Cardinals.
Browner is expected to receive a one-year suspension for substance abuse, but no official announcement has come on his status. The Seahawks signed former San Francisco 49ers cornerback Perrish Cox on Monday and added him to the active roster in place of Thurmond.
Seahawks coach Pete Carroll said he talked to the team about the situation Tuesday morning.
"We dealt with it today,'' Carroll said after practice. "We talked about it in meetings and made sure we owned up to it. We'll take care of business. This team is very strong about where we're going and what we're doing. Just because someone slips doesn't mean we're not on track.
"We're very disappointed those guys will not be able to play with us. It's kind of how it goes at times. I don't know that we can expect to be perfect. We'd like to be, but that isn't the case. You want guys to be on point, but sometimes you're going to be disappointed. It's not about what pops up, it's about how you deal with it and overcome it."
Even though the suspensions could lead some to view the Seahawks as a team out of control, Carroll doesn't believe in giving up on a player who may have a problem.
"We'll always look to give guys a second chance around here," he said. "The fact that the league has adjusted the rules, allowing a guy who is suspended under these circumstances to be with us, we're going to take care of them and look after them until we get them back."
Tate said he was disappointed by the vitriol over the suspensions he read on Twitter from some fans, something he felt didn't represent the team's 12th-man tradition.
"They talk like Tarzan, but they really look like Jane," Tate said of the Twitter commenters. "They write things they would never say to your face. But without these two guys [Thurmond and Browner], we still need the 12s to show Monday night, and we need to show up.''
Seattle linebacker K.J. Wright doesn't think that will be a problem.
"We are the guys who will be out there," Wright said on 710 ESPN. "When we're on the field, none of this stuff is going to matter."