Barnese was one of the aces of the Stone Crabs starting rotation during the 2010 season. He was 8-4 with a 3.02 ERA and 100 strikeouts in 20 starts while being nominated for the Florida State League All-Star Team.
Barnese was drafted by the Tampa Bay Devil Rays in the third round of the 2007 Draft out of High School in California.
He began his minor league in 2007 as a member of the Princeton Rays were he went 2-2 with a 3.22 ERA and 37 strikeouts in 9 games with the P-Rays. In 2008 Barnese was 5-3 with a 2.45 ERA and 84 strikeouts as a member of the Hudson Valley Renegades. He was nominated to the New York-Penn League All-Star team was well as honored as the Renegades Pitcher of the Year. He was promoted to Bowling Green at the start of the 2009 season where he was 6-5 with 2.53 ERA with 62 strikeouts in 15 starts with the Hot Rods.