The home secretary said 5,500 police officers had been on duty on Monday - more than for any other comparable incident in the last 30 years
But as he made a Commons statement to MPs, there was criticism that police chiefs had not taken more action at the first signs of trouble on Monday.
Nine police officers were hurt and 97 people arrested during the protest around Parliament Square and Whitehall in central London.
It is thought the bill for repairing the damage and paying for the emergency services could come to £500,000, with police overtime estimated by Mr Straw at £3m.
Some of those arrested during the protests have appeared in court facing charges ranging from violent disorder, criminal damage and to being drunk and disorderly.
Mr Straw said the "shameful violence" was the culmination of a series of events which took place over the Bank Holiday weekend.
Police inquiry
He said: "What was witnessed in central London yesterday was criminality and thuggery masquerading as political protest.
"In our democracy there is neither reason nor excuse for such appalling behaviour."
The home secretary said 5,500 police officers had been on duty on Monday - more than for any other comparable incident in the last 30 years
He said the commissioner of the Metropolitan Police would be reviewing the incident and the government would respond to any recommendations he makes.
'Back police judgment'
But Shadow Home Secretary Ann Widdecombe said there was "concern about the amount of activity and disorder that was allowed to take place before the police decided it was the proper time for intervention".
She said there would also be concern about "the contrast in the policing methods used during the visit of the Chinese President, when the mildest demonstration was restrained, and what happened yesterday when there was considerable restraint before intervention took place".
But police chiefs have defended the way they dealt with the protest, and Mr Straw said: "If you acknowledge that this was a very, very difficult situation...I think you need to acknowledge that after the event as well as before and back the judgment of the Chief Office of Police and his colleagues, as do I.
"The police did not allow illegal acts to take place. But what they had to do was to make these fine judgments in order to prevent worse disorder and violence taking place."
He said police had decided that handling the situation differently could have seen violence spreading across the West End.
Mr Straw said demonstrators campaigning for workers at the threatened Rover plant at Longbridge had been denied their chance to make a peaceful protest by the "mindless violence" of the anti-capitalist demonstrators.
Miss Widdecombe said those charged following the violence "should face exemplary sentences".
And she said the government should consider banning similar May Day protests in future, and Mr Straw said he would carefully examine any such requests from the police.
'Huge affront'
Prime Minister Tony Blair said earlier that defacing the Cenotaph and the statue of Winston Churchill was "simply beneath contempt".
And Mr Straw said the attacks on the Cenotaph and the Churchill statue were "particularly shocking" and a "huge affront" to those who had fought for their country.
He said: "Without the sacrifice of millions who gave their lives to defend our freedoms, no one yesterday would have been enjoying any right to protest at all."
But organisers of the protest said "the abhorrence of sending millions of men to their deaths in the trenches dwarfs the stupidity of any possible slogan on any possible piece of stone".
John Jordan, an activist from Reclaim The Streets, read out a statement from the organisation at a news conference.
It said: "We respect and celebrate all those people who are, and have been, prepared to stand up to fascism, imperialism and dictatorship.
"That said, we do not necessarily celebrate the generals and the ruling class that sends people to their deaths in order to protect the privileges and control of the few."
'New brutality'
In the Commons, Liberal Democrat home affairs spokesman Simon Hughes praised police for their professionalism.
Labour's Dale Campbell Savours said he was a veteran of many demonstrations in the 1960s but said what was happening now was characterised by a "new brutality" and "ugliness".
He said: "The use of balaclavas and helmets and masks clearly indicates that some people are attending these rallies and demonstrations with only malice in mind."
Tory John Greenway, a former policeman, said the threat was different to anything he had faced while on duty at demonstrations.
He said the British people would never again accept the desecration of the Cenotaph.