Thurmond was suspended for four games without pay for violating the league's substance abuse policy and won't return to the team until Dec. 23.
Browner is reportedly expected to receive a one-year suspension for substance abuse.
"Everyone should realize where this team is," Tate said Tuesday on ESPN Radio. "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."
Tate, who is the team's leading receiver this season, also said he didn't appreciate some of the comments from fans on social media.
"They talk like Tarzan, but they really look like Jane," Tate said. "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.''