It stresses that the UK "must respect" the wish of a majority of the British citizens and has to officially withdraw from the EU by directly triggering article 50.
According to the resolution, "this will allow withdrawal negotiations to start as soon as possible and to prevent prolonged uncertainty for businesses and citizens alike."
The resolution was adopted by a large, nearly two thirds majority at a special session of Parliament on Tuesday.
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It also "stresses that the EU has to reform and needs a treaty revision."
The left-leaning GUE/NGL group, however, refused to back the resolution.
During an often stormy session on the UK's decision to leave the EU, the group made an impassioned plea to the Commission to "change its ways and start listening to its citizens."
Its leader, German MEP Gabi Zimmer, spoke of "the EU's current malaise", adding, "Placebos won't help if the patient is seriously ill. We are talking about the future of the EU and we've seen the erosion process accelerate thanks to Brexit.
"But the EU caravan rolls on. We are not seeing any real self-criticism, any thoughtfulness there. That's why my group is unable to vote in favour of the resolution," she said.
On the survival of the EU, Zimmer said the bloc's leadership was to blame for its current struggles.
"The deep financial and economic crisis has imprinted itself on the consciousness of its citizens."
Zimmer called for a "new social deal" for the EU, with social protection and equal pay for equal work at the heart of its policies, adding, "Margaret Thatcher's original idea that 'there is no such thing as society' has become a dangerous part of EU policy, too.
"It's no coincidence that many of the Brexit supporters are people concerned about social security, pensions and jobs. The EU through its austerity policies hasn't shown that it's concerned about people and the need to protect them from the impact of globalisation."
Polish ECR group member Ryszard Legutko described Brexit as "the worst thing that has ever happened in the history of European integration."
He added, "We have to reflect on how to correct this, Commission as well as Parliament. The picture is not rosy at all and I wonder whether EU leaders will be able to learn from their mistakes."
ALDE group leader Guy Verhofstadt took a tough stance on Britain's EU exit, saying, "We cannot afford to be stuck in limbo. The British must not hold the EU to ransom. Triggering article 50 is necessary, if we are to respect the democratic choice of the British people."
"We should use this momentum to make the EU work again, which means an effective European government for the Eurozone, a European border and coast guard to safeguard free movement, a European capacity to fight terrorism and a defence community.
"The result of this referendum is a wake-up call which we should use to move forward. We will only be able to turn the tide by working more efficiently together."
Meanwhile, European Council President Donald Tusk also says that the will of British voters must be "respected."
Speaking on Wednesday on the second day of a key summit in Brussels, he said, "We all recognise that a process of orderly exit is in everyone's, and especially, in the UK's interest."
Tusk said the decision to trigger article 50 must be taken by the new leadership in Britain.
Speaking about the first day of the summit, he said, "Our discussions were calm and measured. Leaders understand that some time is now needed to allow the dust to settle in the UK.
"But they also expect the intentions of the UK government to be specified as soon as possible. This was a very clear message, which I believe Cameron will take back to London."
Parliament President Martin Schulz said, "Dealing efficiently and swiftly with the withdrawal of the UK from the EU will allow us to put an end to this period of uncertainty.
"It will also allow the Union to concentrate on the different priorities where citizens expect concrete results to be delivered. Although the economic environment has shown signs of improvement, the EU must do better.
"We should be ambitious and aim at strong growth and full employment. We owe this to our citizens, and in particular to the younger generation."