BT took a £34m management fee, and the council incurred staff costs of £43.3m.
The costs marked an increase of £10m on the previous year.
Deputy Labour leader Paul Brant said: “The council needs to work with Liverpool Direct to carry out a proper value for money exercise.
“Questions about rising costs have been bubbling under for a long time now, and the issue needs to be resolved urgently.
“Information technology costs have changed so much since the Liverpool Direct contract was first agreed that council taxpayers deserve assurances that their money is not being wasted.”
Liverpool Direct Ltd was set up as a joint venture with BT, in 2001, to improve the council’s customer services department.
It has since expanded its remit into other areas of the authority.
