Up to 150 people were involved in the demonstration at the Sons and Daughters event, which took place in the former military barracks in Ebrington Square on Sunday evening.
Two men were arrested and charged with disorderly behaviour.
A 22-year-old appeared before Londonderry Magistrates Court on Monday morning and a 30-year-old is due at the same court on 13 February.
The event saw local stars including Girls Aloud singer Nadine Coyle and Snow Patrol frontman Gary Lightbody kick off Derry's year as UK City of Culture.
Police said it was not disrupted by the protests.
A statement said: "Police can confirm that a crowd of approximately 150 loyalist protesters attempted to cause disruption and block roads during the opening UK City of Culture Sons and Daughters concert in Londonderry yesterday evening, Sunday 20th January.
"The policing operation that was in place ensured all main roads in the area remained open and no disruption was caused to the event by the protesters."