Speaking on the opening day of the European Business Summit in Brussels, the Belgian MEP said that events such as Brexit represented warning signs for the EU.
"The EU has to change, otherwise there is the risk it will collapse one day," he told a session debating the future of Europe.
Verhofstadt, Parliament's negotiator on Brexit, told the audience that a domino effect that some had feared after the UK voted to leave the EU had not materialised.
He said, "Public opinion about the EU has, if anything, become more favourable since the Brexit vote and fears of a Grexit or Frexit have simply not happened."
The former Belgian Prime Minister added, "However, the big mistake would be to think that we can return to 'business as usual.'
"It would be a mistake to think that, with the election of a pro-EU president in France, that things can return to normal.
"This is not the case and we need to take heed of what the public are saying: that the EU has to change."
He added, "The future of the EU lies in the hands of a new generation of politicians but they have to realise that the public want change. They are very critical of the way the EU is today and they have every reason to feel that way.
"The people, in elections in the Netherlands, France and elsewhere, have said that they want to give politicians another chance. The public is not against the EU, but just the way it is currently run."
Verhofstadt was also highly critical of the current EU budget which, he said, fell well short of what was needed.
He said the budget for the 28 member states was equivalent to just one per cent of Europe's overall GDP.
He asked, "How on earth can we govern Europe with just one per cent of GDP? Some 80 per cent of the EU budget comes from member states and is paid back, almost immediately, to them. One of the challenges we face is to change the way the EU is financed."