Sinn Fein, however, hit out at the policing operation on the night saying there were "numerous failings" such as "prolonged" stops to the parade.
“The PSNI’s focus tonight should not have been on photo-ops but instead ensuring the most professional and safest policing operation possible," said Mairead O’Donnell.
The Sinn Fein representative welcomed the peaceful passing of the parade but said she would be raising issues with the police locally and through her party's representatives on the Policing Board.
"Frustratingly for residents and community activists working hard to ensure a peaceful evening, there were major failings in the associated policing operation," she continued.
“In recent weeks we have worked hard with the PSNI and local residents to ensure a scaling back of the usual ‘screening-off’ of the parade route. This allowed for less disruption to local residents and traffic in the city.
“Numerous issues presented themselves during tonight’s operation - not least numerous, prolonged stops to the parade itself."
She added: "I want to commend all of those who ensured tonight’s parade passed off peacefully and without major incident.
“Dialogue is required to ensure no such policing operation is required in the future so residents can live without disruption.
“There are many lessons to learn from tonight and the PSNI must learn them.”
The PSNI could not be reached for comment, however, Chief Constable Byrne commended officers on the ground at the parade for their "great and outstanding work" in a number of tweets.
In the strategic coordination centre with ACC Hamilton the Gold Commander for this evenings Battle of the Somme commemoration parade. Great work by @PoliceServiceNI officers who are on the ground keeping the community safe. pic.twitter.com/v1nPZNsJJu