Gavin Rossdale on Wanting to Impress His Kids with His New Music: They 'Inspire Me to Be Better'

"I don't want them to play my records to their friends and say, 'What happened to my dad?'" the Bush frontman tells PEOPLE in this week's issue

While on tour with David Bowie in the '90s, Gavin Rossdale got a piece of advice from the late rock legend that he'll never forget: "Outlive your critics."

With the Bush frontman, 54, and his bandmates' new album The Kingdom — the eighth to be released in the nearly three decades since the band formed in 1992 — out Friday, he realizes he's done just that.

"The people who slagged me off are retired and gone," Rossdale tells PEOPLE in this week's issue, on newsstands Friday. "I was like, 'I did it!'"

These days there are really only four critics Rossdale cares about, anyway: his kids. While writing and recording The Kingdom, he had his sons Kingston, 14, Zuma, 11, and Apollo, 6, whom he shares with ex-wife Gwen Stefani, and his daughter Daisy Lowe, 31, whom he shares with ex Pearl Lowe, on his mind.

"I don't want them to play my records to their friends and say, 'What happened to my dad?'" he says. "I want them to be like, 'My dad's on fire.' They inspire me because I want them to like what I do. They inspire me to be better."

Gavin Rossdale and his sons. Gavin Rossdale/Instagram

Now that his eldest son Kingston is showing a similar passion for music, Rossdale says he's been trying to introduce him to some greats in the punk rock genre, including the Sex Pistols and Gang of Four.

"We're trying all these different bands along with bands from his generation," he says. "Young kids that are making music now, it's cool, but I was like, 'Why don't we look at the beginning? See where it came from.' He's just a joy because when he's playing guitar, all he wants to do is wear my clothes. He comes out looking better than me, generally. Basically all three boys, all my kids, they're just better versions of me. I gave them my strengths."

A benefit of life under lockdown amid the coronavirus pandemic for Rossdale has been the extra time he's gotten to spend with his boys, who have been splitting their time between their dad's home in Los Angeles and their mom's boyfriend Blake Shelton's ranch in Oklahoma. (Rossdale's daughter Daisy lives in London.)

"We've been making a lot of ice cream," he says. "This morning I was playing some PS4 nonsense. I was getting heavily told off for not using controls correctly, but it's good fun. It's important how we hang out and spend time together."

As a father, Rossdale says he's "really tough on matters and how you deal with people."

"I don't like if they're lazy — if they don't read a book, don't talk," he adds. "I'm seen as a bit soft in some regards because I don't want to be annoying, you know? So I respect them and I listen to them and I learn from them as to what they need, but I don't try to be a cool dad. I don't try to be their friend."

With The Kingdom, Rossdale hopes it can serve as a soundtrack to the current uprising against police brutality.

"It really feels like this record is a statement about how we can be better people," he says. "If you listen to the song 'Bullet Holes,' it talks about race wars. The Kingdom, which is the title track, could be the music to the peaceful protests. I can't wait for people to hear it."

Gavin Rossdale. Dove Shore

Overall, Rossdale feels extremely thankful to still be a "working musician."

"My whole goal in my life was to get a record deal," he says. "That's what I thought was the most incredible thing. And that was enough. So to have a record deal and a life and a career is just like, oh my Lord, that's probably why we work so hard. We don't want it to end. We don't want it to go away. We're basically in the dance competition of life, and please don't tap us on the shoulder."

"It's a great life," he adds. "It just blows me away how I still get to do what I love so much."

For more from Gavin Rossdale on fame and fatherhood, pick up the latest issue of PEOPLE, on newsstands Friday.