Chris Cosh, the University of South Florida’s new defensive coordinator, acknowledged he made a difficult decision last week when leaving the same position at Kansas State, but said he was swayed by USF’s potential and the opportunity to reunite with head coach Skip Holtz.

“The future here is tremendous,’’ said Cosh on Tuesday in his first comments since being hired by USF on Jan. 19. “What you have around you is so exciting. All you need is a car or a bike and you’re right in the middle of a great recruiting territory.

“An incredible amount has been accomplished with this program in a very short amount of time. I think we’re on the verge of something very big here.’’

Cosh, 52, was on the South Carolina staff with Holtz from 1999-2003.

Following the 2000 season, the Gamecocks came to Tampa’s Outback Bowl and trained at USF.

“I got to know what Tampa was all about,’’ Cosh said. “It was at the very beginnings of USF’s football program at that time. I knew it had changed a lot, but really, I had no idea how much it had changed.’’

After Bulls defensive coordinator Mark Snyder left for Texas A&M on Jan. 9, Holtz contacted Cosh to gauge his interest in joining USF. It was just three days after Kansas State had lost against Arkansas 29-16 at the Cotton Bowl.

“You’re getting over the disappointment of the bowl loss, jumping into recruiting, then Skip calls and that gave me another thing to think about,’’ Cosh said. “I was excited to get the call. I knew about what Skip has done as a head coach, what kind of teacher and recruiter he is. I wanted to give it a look. When I got here, I was pleasantly surprised by everything that was here.’’

Cosh came to Tampa and attended USF’s football banquet, meeting with the players and staff. He toured the facilities and campus. Then he asked for some time to consider the job offer.

After deliberations that were more difficult that he originally suspected, Cosh told Holtz he would accept the position, which carries an annual salary of $325,000.

Cosh, who recruited parts of Florida for Kansas State, said he will utilize a four-man front. He wants USF “to be a team that runs to the football and makes the tackle. I want us to play with great enthusiasm and emotion. We want to put pressure on people and tackle them when we get there.’’

After viewing some film from USF’s 5-7 season, he said the Bulls “aren’t far away from doing big things’’ and his defense returns a “very good nucleus of players.’’

“The future here is bright,’’ Cosh said. “I’m glad to be part of it.’’

Cosh’s Kansas State defensive unit drastically improved its rush defense last season, moving to 37th nationally (131.2 yards per game) and finishing 119th (out of 120 Football Bowl Subdivision schools) in 2010. Last season, Kansas State was ranked 103rd nationally in pass defense (263.4 yards per game) in the offensively potent Big 12.

The Bulls, who failed to make a bowl game for the first time since 2004, were 39th overall in defense last season, allowing 351.3 yards per game. In Big East Conference games, the Bulls were seventh among eight teams, surrendering an average of 379 yards.

The Bulls suffered several fourth-quarter meltdowns in 2011, giving up last-minute drives to Miami and West Virginia, which led to final-play, game-winning field goals. They also allowed a last-minute drives in narrow defeats against Cincinnati and Rutgers.