While the Dolphins instead named defensive back Minkah Fitzpatrick with the 11th overall pick, Gase told PFT Live that Tannehill wasn't sweating the decision. His attitude, Gase said, is focused only on things he can control.
"He's one of those guys who's going to worry about himself and keep working. He's not going to worry about what's going on outside," Gase said.
Tannehill is aiming to show he's back to form this season after missing the entire 2017 campaign with a knee injury.
"Expect a guy that's extremely hungry to get back on the field and lead this team," Gase said of Tannehill. "I think there's an appreciation for him after him not being here last year and guys are excited for him to get this thing going."
Tannehill should be close to full health when the Dolphins hold organized team activities next week. He is expected to participate in OTAs with little or no limitations, the Miami Herald reported Tuesday, citing team sources.
Miami could opt to tread cautiously with Tannehill and give the bulk of the snaps at OTAs to backups Brock Osweiler and David Fales.
Tannehill initially injured his knee against the Arizona Cardinals in December 2016, partially tearing the ACL. It was re-injured on Aug. 3, when he fell to the ground while scrambling toward the sideline in practice.
The 29-year-old Tannehill has started 77 games for the Dolphins over five NFL seasons. His 62.7 career completion percentage is second in team history and his 86.5 career passer rating is third among all-time Dolphins quarterbacks.
Tannehill had his most efficient season as a professional in 2016, his first under coach Gase, completing 67.1 percent of his passes for 2,995 yards, 19 touchdowns and 12 interceptions with a career-best 93.5 passer rating in 13 games. He originally joined the Dolphins as a first-round pick (eighth overall) in the 2012 NFL Draft.