Labour council chief Sarah Bogle said the disorder earlier this month had attracted global attention.
She said Southampton needed to rebuild and show the best of the city after a “really difficult week”.
Disorder broke out on the evening of June 2 following the release of police bodycam showing 18-year-old student Henry Nowak being placed in handcuffs after he was stabbed by Vickrum Digwa.
Digwa, 23, was jailed for Mr Norwak’s murder.
Cllr Bogle was asked about the protests, which have resulted in more than 20 people facing criminal charges to date, at Southampton City Council overview and scrutiny management committee.
She said: “Firstly, I just feel we need to honour Henry Nowak’s family and the words that his father spoke outside the court.
“Sadly, the events of June 2 did not reflect his wishes and somehow, we need to rebuild from what has been a really difficult week for the city and it’s put us on the map for all the worst reasons.
“I’m proud of this city. We’re a tolerant city, we generally get on, we are a diverse city, we have got 160 languages.
“This is being fermented and wound up as it were.
“It is really tragic and it is horrible that an awful, awful tragedy like Henry’s death has been weaponised like this.”
Cllr Bogle, who became council leader on May 20, said she wanted to try to move forward and put an arm around the city, particularly in Portswood.
She added: “I’m keen to try and find ways to move on and show the best of Southampton and change the story about Southampton because we have got a lot of things to be really proud of as a city and a lot of good stories to tell.
“We are all a part of that next stage because this has been unprecedented.
“We’ve literally become a global sensation last week.
“It was a bit of a baptism of fire for me definitely.”
Green Party group leader Matt Renyard said it was important Cllr Bogle had shown leadership since the protests.
Councillors across political parties needed to come together at a time when there were genuine fear among communities, he added.
Cllr Renyard said: “More generally, this is not the Southampton city that we know and love.
“We are a very united and diverse community and that’s always been one of our strengths because we’ve always been a city of sanctuary, a city that is connected internationally around the world and that’s welcomed people from far and wide.
“Whilst these events are incredibly tragic, we need to make sure that we find a way to heal our way through that.”
Cllr Bogle said a lot of work was being carried out by interfaith groups.
She praised the work of everyone involved in the clean up the day after the violence and committed to do all she could to defuse tensions.
The Bargate ward member added: “There’s a lot of damage to undo and there’s a lot of rebuilding to do but I believe Southampton can bounce back.
“We’ve got a resilient community and we’re a strong city and I’m sure we can pull together.”
Reform UK councillor Soham Bandyopadhyay said he been speaking with residents, particular in the Sikh, Hindu and Muslim communities, to reassure them that none of the protests had been directed at them.
He said there had been miscommunication over who the protests were directed at.
Cllr Bandyopadhyay: “It might be useful for the council also to clarify that none of the protests are against any specific skin colours or faiths currently.”
Cllr Bogle said most of the “hatred” had been directed towards the police.