The 'Blow Me (One Last Kiss)' singer and husband Carey Hart welcomed daughter Willow in June 2011, an experience which has left the star afraid of making a mistake.
"I'm a perfectionist, I cry daily! I'm glad though, that the two things that have gone wrong were Dad's fault!" Pink joked to Entertainment Tonight Canada.
"The first time anything bad happened he was like, 'Oh, I'm so glad it was me!' I'm like, 'Me too! I'm going to cry anyway though'."
Pink also shared her enthusiasm at having been recently named the new face of CoverGirl cosmetics, saying: "I thought they were kidding. My manager called and said, 'CoverGirl got in touch', and I was like, 'Yeah, right. I'm busy! I've got to change a diaper'.
"But then they were serious and I was flattered! Very honoured. I like the team! I like the ladies that they use. Everyone is very different and powerful in their own right."
> Pink rejected 'X Factor', 'Idol', 'The Voice': 'People would hate me'
Watch Pink's video for 'Blow Me (One Last Kiss)' below: