Prior to his stint at UAB, he coached the defensive line of the Tulane Green wave for three years.
While at UAB, Costantini helped develop defensive tackle Elliott Henigan into an all-conference performer. Costantini also has spent time at two other C-USA schools before they became league members. He served on the staff at UCF from 2000-03 and at his alma mater, UTEP, from 1995-99.
While at UCF, his 2002 defensive line ranked third in the Mid-American Conference with 31 sacks. The 2000 and 2001 editions of the Golden Knight defense ranked in the top 30 in the nation.
At UCF, he coached a pair of players who went on to the NFL in Elton Patterson, an All-MAC selection who was a seventh-round selection of the Cincinnati Bengals in 2003, and Josh McKibben, who signed with the Baltimore Ravens.
Costantini was a four-year letterwinner as a defensive tackle for the Miners from 1986-90 and graduated from the El Paso university in 1990. He began his collegiate coaching career at UTEP in 1995 as the team's strength and conditioning coach and was promoted to defensive line coach a year later. At UTEP, Costantini coached four players who earned All-Western Athletic Conference honors eight times during their careers.
Topping the list was Brian Young, the 1999 WAC Defensive Player of the Year and a three-time All-WAC choice. He was a fourth-round NFL selection of the St. Louis Rams.
Costantini attended high school in Houston before moving on to college at UTEP. He was a member of the Miners' team that won a school-record 10 games and earned a trip to the Independence Bowl in 1988.
Costantini and his wife, Merritt, have a 8-year old son, Rocco, and a 7-year old daughter, Sofia.