The club said revenue fell year-on-year by more than 30% to £31.3m for the six months to the end of December.
Pre-tax profits also fell substantially, from £21.3m to £6.6m.
Celtic were knocked out of the Champions League in August after losing to Slovenian side Maribor. They are currently playing in the UEFA Europa League.
The club also cited lower gains from the sale of players as a reason for the poorer trading performance.
Revenues from multimedia and other commercial activities fell from £19.5m to less than £8m, while merchandising revenues also dropped.
In a statement, chairman Ian Bankier said: "As in previous years, the second half is expected to be more challenging in terms of financial performance with fewer home matches scheduled and no certainty on any further gains on the disposal of player registrations.
"Our strategy remains to live within our means.
"The football environment in Scotland continues to be challenging and we must operate within it in a fashion that does not unduly risk the long term future of this great club.
"Our key focus for the remainder of the year will be to build on the progress we have made in the first half of the season and to deliver silverware from competing in the three domestic competitions and remain competitive in the UEFA Europa League."
Celtic have attributed a sharp fall in revenue and profits to their early exit from the UEFA Champions League.