The star has teamed up with the British artist for new track 'True Love', which features on her forthcoming album The Truth About Love.
"I met her for the first time after the song was recorded, but I'm a super fan of hers," Pink told Capital FM.
"Greg Kurstin was our common thread - he did her last album It's Not Me, It's You. I just met her for the first time when she came and sang that song with me on VH1 Storytellers."
She added: "It was very strange to meet someone for the first time on stage, but I think she's awesome - she's so sweet."
Pink's new album The Truth About Love will be released in the UK on September 17 and a day later in the US.
Listen to Pink and Lily Allen's 'True Love' below: