England beat Sri Lanka by five wickets in Hambantota, but the hosts' 35 overs went more than 20 minutes over time and now Cook faces a suspension if found guilty of a slow over-rate .
Cook, who was fined for a similar offence after a one-day game against India in August, and told that he would be banned for any repeat within 12 months, admitted that England probably were a little bit slow, The BBC reported.
ICC match referee David Boon would decide whether to apply a ban, although he could spare the England captain depending on how much time was lost for reasons outside his control.
Cook said that he was aware of the possibility of a suspension coming into the seven-match series, but suggested that the size of the ground and the slow rate at which Sri Lanka's batsmen came to the crease were also a factor in how long the innings took to complete.
He said that it's incredibly hard when the ball's flying everywhere, adding that one has to bear in mind how big the ground is. He also said that the batsmen take quite a long time to come out, adding that they knew that coming in, and tried to be as quick as they could.
Cook said that he doesn't know what the punishment would be, if there is any.
Despite the victory, England coach Peter Moores faced criticism from Kevin Pietersen afterwards.
Former England batsman Pietersen, who was effectively sacked by the national team in February, called Moores a woodpecker and blamed him for the poor form of Eoin Morgan, who dismissed for a single run.
Pietersen suggested that the coach could have a negative effect on Moeen Ali, too. He tweeted that Morgan is a free spirit with a woodpecker as a coach, adding that he is afraid it would hurt his spirit.