The former Arsenal defender, who has two weeks to appeal against the ban, can only get it lifted if he pays the money outstanding.
"I feel a little bit let down by the situation because we didn't know anything about it and we couldn't intervene in the end," Allardyce told reporters.
"There will still be a slight door open if he can resolve the situation in the next few days because we've spent a huge amount of time getting him fit and ready for the first-team."
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Sunderland sacked their England winger Adam Johnson in February after he pleaded guilty to sexual activity with a 15-year-old schoolgirl.
The club were heavily criticised for allowing Johnson to keep playing for them despite him confessing to kissing the girl. Margaret Byrne resigned as chief executive three weeks ago over her role in the decision.
Sunderland, third-bottom in the Premier League and two points adrift of safety, host 11th-placed West Bromwich Albion on Saturday.
(Reporting by Shravanth Vijayakumar in Bengaluru, editing by Ed Osmond)
