The 'Raise Your Glass' singer saw footage of Alexander's performance for the first time this week while backstage at Alan Carr: Chatty Man.
"She's cute," said Pink as she was shown a picture of the contestant during her interview. When the audience began to boo, she admitted that she previously "[didn't] know anything about it".
"I think it's interesting that the one person who impersonated me has to attack the set and be an a**hole!" she laughed.
Pink went on to say that although she is not up to speed with UK talent shows, she respects Simon Cowell.
"I think he's brilliant," she told Carr. "He's great, honestly.
"He's a very smart man and it's his thing. It's not my thing, [though]," she added, implying that she wouldn't like to be part of a judging panel.
"I'd rather eat cheesecake and drink wine and play with my kid."
Pink - who revealed that she used to train for eight hours each day as a young gymnast - also took the opportunity to praise the way London hosted this summer's Olympic Games.
"I thought it was awesome," she said. "I thought this Olympics was amazing - number one, because the whole world was paying attention in a way that I didn't feel like they had in previous years... I think that had a lot to do with London and how much the community came together, It was so beautiful.
"It was gorgeous. I was like, 'I performed there! I performed at that one right where that guy just walked'! In my kitchen at 10 o'clock it was all about me."
Pink's new album The Truth About Love is out on Monday (September 17). Earlier this week, she unveiled a lyric video for her duet with Lily Allen that features on the LP and described herself as a "Lily Allen superfan".
Listen to Pink and Lily Allen's track 'True Love' below: