The comment by the public services minister led Plaid Cymru to vote against the Public Health Bill, which included a partial ban on e-cigarettes.
One Plaid AM has called Mr Andrews' attitude "wholly offensive".
But Carwyn Jones said it was a joke and that Plaid had not acted maturely and "people say things in the chamber".
Meanwhile, doctors and nursing unions have called on political parties "not to play games with the health of the nation".
Mr Jones told S4C's Newyddion 9: "People say things and if they had their time again they would say things differently. But to react in this way... that is not a mature response."
"If Leighton had his time again I know he would say something different.
He said Mr Andrews had "offered to apologise, but no".
"Plaid Cymru said they would vote against this no matter what happens with any sort of apology," he said.
As well as a ban on e-cigarette use in some public places, the bill aimed to create a compulsory licensing system for tattooists, ban intimate piercing of children under 16 and require councils to produce a local toilets strategy.
Plaid originally planned a free vote and some of its AMs were expected to support the bill on Wednesday evening, although a greater number were in opposition.
But the party's last minute decision to vote against it as a group meant the assembly was tied 26-26 and the legislation failed.
But Dafydd Elis-Thomas told BBC News he was not informed about Plaid's decision. He had made arrangements to cancel his assembly vote.
"I did not imagine that by not being present I would have helped to lose a piece of important Welsh legislation," Lord Elis-Thomas said.
"I've experienced many low points in this fourth assembly in my relationship with the party, but this is the lowest."
He said he and party leader Leanne Wood, who was against the ban, agreed to not attend the vote - known as pairing - meaning their absences would cancel each other out from the tally.
A Plaid Cymru spokeswoman said: "Dafydd Elis-Thomas had asked to be paired so that he could be in the House of Lords.
"Therefore he wasn't in the group meeting [Wednesday] afternoon when the unanimous decision was taken."
Leighton Andrews would not repeat a jibe about a "cheap date" if he had another opportunity, the first minister has said.