But they are yet to charge anyone for the coin-throwing incident which saw Manchester United defender Rio Ferdinand hit by an object at the end of the match.
Ferdinand was celebrating Robin van Persie's late winner but was left with a gash above his eye after the incident.
Two men have been charged with pitch encroachment.
Chief Inspector Steve Howard said: "To have just 13 arrests for a crowd of this size and a match of this proportion is a testament to the policing operation we put in place.
"Despite fierce rivalry and high tension there was no major disorder. However, we will continue to investigate the coin throwing incident and are determined to work with the club to bring the perpetrator to justice."