"We can't buy into all that. I believe that it's disrespectful," Landry said, according to ESPN.com's James Walker. "A man that comes out here and works his butt off and for people to not understand what's really going on or to not have even touched the field before say 'We want somebody else to be playing,' and they don't understand the situation or know what's going on."
Landry's comments come after some fans at Hard Rock Stadium chanted "We Want Moore" in hopes of seeing backup Matt Moore take over for Cutler.
Landry added he thinks fans like that "just want to be on Twitter."
Through four games, the 2-2 Dolphins rank last in the NFL with 156.5 passing yards per game as Cutler has struggled to find his footing in Adam Gase's offense.
All told, Cutler has completed 62.6 percent of his passes for 706 yards, three touchdowns and three interceptions. His 5.4 yards per attempt and quarterback rating of 74.8, meanwhile, rank 31st and 30th, respectively, among qualified passers.
Cutler and the Dolphins' passing attack will attempt to get on track Sunday against the Atlanta Falcons' 17th-ranked pass defense.