Cobb was 3-0 with a 2.05 ERA and 29 strikeouts in four starts at Durham before making Sunday's start for the Rays, in which he threw 4 1/3 innings and allowed four runs on four hits and four walks to earn a no-decision.
"The whole experience was amazing," Cobb said. "The past two days have been just a blur. Next time I get the call, hopefully it will go a lot smoother and won't be as rough of a transition."
Cobb, who hails from Vero Beach, Fla., had approximately 40 family members and friends in the stands. Included in the group was his brother, Richard, who is in the Army and stationed in Missouri after serving in Iraq, where he was wounded and awarded a Purple Heart.
"That meant everything to me," said Cobb about his brother attending the game. "I've seen him like five days over the last three years."
Cobb's start was made necessary by Wade Davis getting pushed back a day due to Tuesday's rain-out in Minnesota.
Rays manager Joe Maddon remains a big fan of Cobb.
"Overall, I like his stuff a lot and think he's going to be a very competitive Major League pitcher," Maddon said.
The Rays will need to make another roster move with a position player prior to Tuesday's game. Evan Longoria (strained left oblique) will play the final game of his rehab assignment at Double-A Montgomery on Monday night. He is expected to fly to St. Petersburg on Tuesday morning, in time to join the team for their 6:40 ET game against the Blue Jays.