Basil Khan and Omar Mohidin were 16 when they were hit and racially abused by officers in Edgware Road, north west London in 2007, the High Court heard.
The sergeant and a constable involved were acquitted along with four colleagues in a criminal trial in 2009.
The High Court ruled the two men were racially abused and awarded damages.
The Met's Deputy Assistant Commissioner Fiona Taylor said the officers' actions had let down the public and all of the force.
Officers from the Territorial Support Group stopped the teenagers in June 2007 because they claimed that some of the group had been mouthing obscenities and making gestures at them.
Omar Mohidin was held in a police van for about five minutes while officers arrested Basil Khan who was handcuffed, strip searched and held in police custody for almost 20 hours.
Mr Justice Gilbart said Mr Khan had been wrongfully arrested and he accepted PC Mark Jones, who has since left the force, had hit Mr Khan, grabbing him around the neck and making it difficult for him to breathe.
The judge awarded Mr Khan £11,900 in damages and said Sgt William Wilson had also struck Mr Khan.
The court ruled Mr Mohidin was also falsely imprisoned for a few minutes during which time he was subjected to "racist humiliation", but that his injury amounted at most to feeling upset for a few days.
He dismissed Mr Mohidin's claim that he had suffered acute stress disorder as a result of the police action and awarded him £2,500.
The judge threw out a third civil damages claim for false imprisonment, assault and race discrimination brought by another man, Ahmed Hegazy.
The Metropolitan Police Service has been ordered to pay more than £14,000 in damages to two men of Arab origin for racially abusing them as teenagers.