Speaking on Monday, he said he did not want to "downplay the economic costs" that would accompany a potential Brexit.
He added, "I have no doubt, however, that we (member states and EU institutions) are already prepared for the day after the referendum."
The former Polish Prime Minister was speaking after a meeting in Lisbon with the Portuguese Prime Minister Antonio Costa.
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Afterwards, Tusk said that while he hoped the UK would remain a part of the EU, "Whatever the result is going to be, we must take a long, hard look on the future of the Union. We would be foolish if we ignored such a warning signal as the UK referendum. There are more signals of dissatisfaction with the Union coming from all of Europe, not only from the UK."
Tusk is due to chair a summit of EU leaders and heads of state in Brussels next week where the outcome of Thursday's UK referendum will come under the spotlight.
He added, "I would like to appeal to the British citizens, on behalf, I know that for a fact, of almost all Europeans and European leaders: Stay with us. We need you. Without you, not only Europe, but the whole western and transatlantic community will become weaker. Together, we will be able to cope with increasingly difficult challenges of the future. I am absolutely sure about this. If apart, it will be more difficult."
His comments come with latest opinion polls showing a major surge in support for the Remain camp. This comes in the wake of the brutal murder last week of British Socialist MP Jo Cox.
Tusk's message was not entirely shared by German ALDE group MEP Alexander Lambsdorff, who, speaking at an event in Brussels on Monday, said, "The EU is imaginable without the UK but not without Germany or France. The UK was not in at the beginning and they are just too peripheral for their membership to be the determining factor [in the EU succeeding or not]."
He added: "Creating incentives for leaving would be a fundamental mistake," in reference to how exit negotiations should be handled, if needed.
Elsewhere, Giles Merritt, founder and Secretary General of leading Brussels-based think tank, Friends of Europe, said, "Whether or not the UK votes to stay in the EU, the Brexit referendum is damaging the EU project. And this, to a large extent, is not so much the fault of the British but of the EU and its Brussels-based institutions themselves."
He added, "Faith in the value and achievements of the EU is evaporating fast. The latest opinion survey by the Pew Research Centre in Washington, DC showed a drastic slide in the EU's popularity; as almost half the 10,000-plus people surveyed across the EU this spring are now broadly Eurosceptic.
"This from the same research centre which branded the EU as 'the new sick man of Europe' several years ago."
Merritt, a former Brussels bureau chief with the Financial Times, added, "Pew's pulse-taking of support for the EU has won widespread recognition as fair and unbiased - not an accolade awarded to all of the surveys conducted by the EU's in-house Eurobarometer that collates national poll findings.
"So the latest finding by Pew that on average 47 per cent of Europeans have an unfavourable view of the EU is not to be taken lightly.
"The big surprise is that in France, a remarkable six per cent of opinion has turned against the European project, which the French once did so much to create. Negative opinion in Germany is also on the rise, standing at 48 per cent, which (also surprisingly) is broadly the same as in the UK."