The 28-year-old, whose wife Kim Sears gave birth to their first child in February 2016, said he'd "rather be a good dad" than win every tennis match.
Speaking as a TV pundit, Croft said he "generally looked exhausted" and the "pressure of raising a child" was showing on court, according to the Daily Star.
"I would rather be getting up in the middle of the night and helping Sophia than winning every tennis match and her thinking when she grows up, 'Actually, you know what, he was a s****y dad but he won a lot of tennis matches, so well done'," Murray said, according to The Mirror.
Murray felt the need to respond to the criticism after he'd read an article which he said "sort of" blamed Sophia for him losing the Miami match.
"That’s actually a horrible thing to say about someone," he said.
"Becoming a parent is life-changing and if it helps my tennis, great and if it doesn’t, that’s fine."
"That’s not a problem for me now. My priority is to be a good father first."
Speaking about becoming a dad back in August 2015, the former Wimbledon champion said:.
"I'm not thinking what the impact [of becoming a father] will have on my career. I'm more concerned about the baby being healthy.
A month after Murray's wife gave birth to Sophia in February 2016, he opened up about the one thing he found "difficult" about being a dad.
"The only thing I found difficult was changing her because you see a small person and you think they’re so fragile," the Tennis star told The Guardian.
"Their hands are so small that when you’re putting their fingers through their top you think they could maybe break."