The deficit for the year to June 30, 2021 was more than £7.5m bigger than the 2019-20 campaign.
The “total comprehensive” loss after tax, player sales and finance costs were taken into account was £26m.
Rangers reported a profit on player registrations of £1.7m but finance costs were £3m.
Revenue was down by almost a fifth at £47.7m while operating expenses were down by £4.5m. The decrease in expenses was “driven mostly by the reduced need for matchday costs”, according to chairman Douglas Park.
Park added in the club’s annual report: “The year under review was of course heavily affected by Covid, and the impact that had on revenue streams, both matchday and non-matchday.
“Initial estimates are that the adverse effect on revenues was over £20m, and the effect on the net loss over £10m.
“The group has submitted a claim on its business interruption insurance for losses caused by Covid, the curtailment of the 2019/20 season and the closed doors games and the restrictions on stadium usage throughout the 2020/21 season.
“The scale and timing of any future claim is uncertain, however we have recognised amounts received from our insurers against our claim to date.”
The annual report added that Rangers are expected to require £7.5m in funding by the end of the season to meet liabilities but the board has reached agreement with Park and fellow director John Bennett to provide loan facilities to meet the shortfall.