"Every year I've been here we were always one piece away, one situation away to where we could turn a losing season to a winning season," David, a 2013 All-Pro selection who appeared in the Pro Bowl for the first time last season.
"We're tired of losing," David, who signed a five-year, $50.25 million contract in 2015, said, adding he and McCoy both are driven to enjoy more team success.
"I've never seen somebody so angry (after a loss), and it shows the type of leader he is," David said.
"He puts everything on himself, puts everything on his shoulders. Me and him feel like we have to put it in our hands and change everything because we are kind of like the older guys on defense. Our main thing is just get everybody on board, and I feel like we're doing that."
Tampa Bay was 10th in total defense last season, with McCoy leading the team with 8½ sacks and David finishing with a team-high 147 tackles, three sacks, three interceptions, two forced fumbles and two fumble recoveries.
But despite ranking among the leaders in fewest yards allowed per game, the Bucs were 26th in points allowed and missed the playoffs with a 6-10 record that cost former coach Lovie Smith his job.
Dirk Koetter, promoted from offensive coordinator, is the fourth coach the franchise has had since last appearing in the playoffs under Jon Gruden in 2007.
David said the transition, with Koetter guiding the offense and former Atlanta coach Mike Smith taking over the defense, has been fairly smooth.
"Everybody is different, their own personality, the way they coach, and how they do different things and how they see things," David said.
"But the great thing about it is these coaches, they really like to interact with you, asking you what you see out there — like what's wrong, what you don't like, what you do like, things like that — and try to make you comfortable the best way they can," he added. "Guys really appreciate and like that."
With middle linebacker Kwon Alexander coming off a strong rookie season and veteran Daryl Smith joining the team in free agency, the Bucs feel much better about their linebackers as a group than entering training camp a year ago.
David said players are more confident, too.
"Not just the old guys, but the younger guys," he said. "They're getting real comfortable."
But no one's more upbeat or optimistic than David.
"I think it's just getting accustomed with everything all around," the linebacker said.
"As I go into my fifth year, I'm getting comfortable with being in the NFL, taking over the role of being a leader, knowing how the guys look at me as a leader and stuff like that," David added.
"So I have to carry myself in a certain way. I noticed that if I'm down, certain guys might be down. If I'm up, everybody's up. I look at things like that, just try to stay positive as much as I can and keep my energy level high."