Speaking in Strasbourg, the former Belgian Prime Minister said the EU had to be "more effective" in the future.
Verhofstadt, who is Parliament's chief negotiator in the Brexit talks, said the result of the EU referendum and also Trump's upcoming presidency showed it was necessary for the EU to be "stronger and more effective."
He said the problem was not with Europe but, rather, a public distrust of "how the EU currently works."
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"The EU is seen as this loose confederation of nation states which is always acting too little and too late."
He was critical of Trump who, he said, "stands for more protectionism."
On Brexit, Verhofstadt said he believes it is still possible to forge a "new relationship" between the EU and UK.
However, he repeated his mantra that the EU "will, on no account, give up on its four freedoms."
The Belgian MEP also said it would be necessary for the UK to accept freedom of movement, one of the EU's four pillars, in any debate about it remaining in the single market.
Further comment on Brexit came on Wednesday when UK finance minister Philip Hammond announced his autumn budget.
Hammond said, "While the Office for Budget Responsibility (OBR) is clear that it cannot predict the deal the UK will strike with the EU, its current view is that the referendum decision means that potential growth over the forecast period is 2.4 percentage points lower than would otherwise have been the case.”"
Separately, the head of Open Europe's Brussels office, Pieter Cleppe, discussed Belgian Prime Minister Charles Michel's meeting with Theresa May on Belgian radio, saying "Given how a bad deal for Britain would entail tariffs and thus also job losses, quite a few jobs on mainland Europe would be lost, so it's in both sides' interest to secure a friendly Brexit."
Meanwhile, a BMG opinion poll has found that 43 per cent of Scots would accept Scotland remaining inside the EU if this meant a 'hard' border with the rest of the UK. However, 57 per cent would prefer Scotland to be outside the EU if that meant it could retain free trade and open borders with England, Wales and Northern Ireland.