Dissident republicans have been blamed after a masked gang hijacked a car and ordered the driver to deliver the bomb to the Victoria Square shopping centre on Sunday night.
The driver took the device into the city and managed to raise the alarm.
In the resulting security alert the bomb partially exploded while army bomb disposal experts attempted to defuse the device.
Mr Ó Muilleoir told UTV: "The people of Belfast have united against this small, small, small minority - this little micro-group of wreckers.
"There was an attack on our city, on our community and I have been really lifted by the response of the people and they won't be deflected or diverted.
The Sinn Féin politician added: "We are very fortunate that we survived last night without any loss of life or any injury but the response to those who try to intimidate and bully us must be that we continue as normal and we resolve to have a great Christmas.
"Christmas is about children and they are the future and I think the message that I am getting today and I have seen overnight is that we are going to have a great Christmas and make sure that the wreckers don't succeed."
This was an attempt to intimidate, to frighten and to threaten the people of Belfast.
Máirtín Ó Muilleoir
The Lord Mayor said he had met with the police to discuss security around the city in the run-up to the festive period.
And the PSNI has said it is increasing police patrols around the city centre in the coming weeks.
Chief Superintendent Alan McCrum said: "There will be a very visible police presence in Belfast city centre over the coming weeks in key locations, at key times.
"Police will be on foot, on bikes and conducting vehicle check points in hot-spot areas to prevent crime and reassure shoppers, revellers and motorists.
"The Christmas period is a time of the year when we see a significant increase in the numbers of people visiting the city, during the day and in the evenings to shop and socialise.
"Police are encouraging people to stay safe this Christmas; keep their own property safe, be responsible about personal safety and actively keep their communities safe by looking out for others."
Chief Superintendent McCrum called on the public to help fight the terrorist threat.
He added: "We are all aware of the threat that is posed by terrorists.
"Police are committed to keeping communities safe.
"The public can help in this process by working with and supporting police as they seek to prevent harm and ensure that Belfast remains a safe and vibrant city to visit."
Everyone can play a part in helping to tackle the terrorist threat by remaining vigilant and by reporting any suspicious activity or behaviour to police.
Chief Superintendent Alan McCrum
Mr Ó Muilleoir said the people of Belfast would ensure Christmas was a great celebration.
He added: "These wreckers will not stop the people of Belfast.
"We need to put it in to perspective, we are very resilient people.
"The PSNI are going to take to keep the city safe and my feeling is that people will just get about their normal business.
"I will be in the city centre shopping on Saturday, I am there in the city hall every day.
"The people of Belfast are not going to give in to these micro groups who have no mandate and really they just need to go away.
"This is not a setback, I see it as a little warning to us about the importance of building peace.
"We need to consign to the dustbin of history those who would drag us back to the past.
"But I am not overly concerned because I saw the response of the PSNI, I think they are really on top of their game."
On Saturday, a group called the Loyal Peaceful Protesters is staging a protest in the city centre against the council's decision to restrict the flying of the Union flag at city hall.
The Sinn Féin Lord Mayor told UTV he held no concerns about the event and felt Belfast could accommodate the occasion.
He added: "I think we are going to have a protest in the city centre which is going to move out of the city centre at a reasonable hour.
"I believe it is a big enough city. If some people want to protest we can accommodate that and I don't think it is going to make any impact negatively on the city.
"Other people have other views about whether it should go ahead or not.
"From my point all I am saying is let's accommodate the protest as a big city and let's get on with Christmas."