Mr Hanvey was elected despite losing the support of his party, the SNP, in the run-up to the vote.
In a statement yesterday, Ms Laird said it had been an honour to serve as deputy leader, but delivered a parting shot to those in the party who she accused of “washing our differences in public” as a means of “self-promotion”.
She also urged a period of “calm reflection and kindness” to one another.
The former shadow Scottish secretary said: “I have seen many leaders of the Labour Party come and go.
“Not all were my choice – but I always took the view that they were our elected leader and my role was to serve the Labour Party as best I could.
“Whatever the challenges ahead, I will continue to serve our wonderful Labour Party in whatever way I can, because fundamentally we are, and must always be, here for the many.”