His team mates were fined 10 per cent after England were found to be one over short of its target.
"Andy Pycroft of the Emirates Elite Panel of ICC Match Referees imposed the fines after the side was ruled to be one over short of its target when time allowances were taken into consideration," the ICC said in a statement.
"In accordance with the regulations of the ICC Code of Conduct for Players and Player Support Personnel (the Code) governing minor over-rate offences, players are fined 10 per cent of their match fees for every over their side fails to bowl in the allotted time, with the captain fined double that."
Play in the match, which ended in a dramatic draw on Monday when the visitors finished at 201-9 after losing six wickets in the final session, went beyond the 6pm official finishing time on each of the five days, with 17 overs lost in total.
At the post-match news conference Cook said the slow over-rate was not ideal, but it hard to manage with four fast bowlers in the side.
(Reporting by Josh Reich)
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