Morris was set on adding Stocker from the start, calling him a potential first-round talent, but patiently waited until general manager Mark Dominic pulled the trigger.
"The nervous head coach sat there and he wants to get guys, and Mark and his staff were right on the details about where they should go and waited until possibly the last minute to take some of those guys," Morris told the St. Petersburg Times on Saturday.
"When you get a Luke Stocker in the fourth round, when you could easily give him the grade of a second-round pick or arguably a late first, that is a phenomenal day," Morris said.
Stocker was the first offensive player taken by the Bucs, who used their first three picks on a pair of defensive ends and a linebacker.
The 6-foot-5, 253-pound tight end had 39 receptions for 417 yards and two touchdowns at Tennessee last season and figures to line up opposite Kellen Winslow in two-tight end sets.
The Associated Press contributed to this report.