The team announced during the game that Cobb was dealing with a foot injury, while Stills suffered a leg injury. Ian Rapoport of NFL Network later reported Cobb has a "significant" toe injury and could miss time.
Based on production this season, Cobb is a bigger loss after entering the day with 36 catches for 434 yards and two touchdowns.
The 30-year-old failed to deliver in his final season with the Packers in 2018 with 38 receptions for 383 yards and two touchdowns in nine contests, but he helped rebuild his value last season in Dallas with 55 grabs for 828 yards and three touchdowns as the Cowboys' No. 3 receiver behind Amari Cooper and Michael Gallup.
Cobb has struggled through multiple injuries in recent years, as he hasn't appeared in all 16 games since the 2016 season.
Stills has also dealt with health problems, missing three games last year, but his on-field issues are a bigger concern this year while totaling just 11 catches for 144 yards in his first nine games.
Although the 28-year-old was a reliable player last season with 561 receiving yards, he has fallen down the pecking order in 2020.
The Texans traded DeAndre Hopkins to the Arizona Cardinals during the offseason, but they are still fairly well stocked at wideout, as quarterback Deshaun Watson will get to lean on Brandin Cooks and Will Fuller V with Cobb and Stills out.
Keke Coutee could also see extra snaps going forward.