Pizzorno told NME that the cover, which Del Rey performed for BBC Radio 1's Live Lounge, is "f**king beautiful" and "a really nice gesture".
He said: "I'm really proud. Obviously we covered one of hers, 'Video Games', so it was quite a sweet thing to do back. It's a really nice gesture. It's proper old-school."
Del Rey has said that she found Kasabian's music through former boyfriends.
"All of my boyfriends had loved Kasabian and I'd never listened to them," she explained. "I started and I really like this song. I love this song and I love the melody, I love the way the boys sing it."
Del Rey posted two enigmatic tweets on Saturday which many have taken as confirmation that 'Carmen' will be her next single.
> Lana Del Rey producer: 'Label didn't want Video Games single'
> Lana Del Rey: 'Blue Jeans' - single review
Watch Lana Del Rey perform 'Goodbye Kiss' below: