Speaking at a press conference in Strasbourg on Wednesday, Schulz praised the outgoing Greek presidency for its "excellent cooperation".
He said, "I want to make it perfectly clear to you I have not seen a presidency get down to work the way the Greek presidency has done."
The S&D deputy continued, "I haven't seen a presidency sign so many documents, I could even counterfeit Mr Samaras' signature myself, it's a sign that we've worked very hard.
"I really would like to recognise that the Greek government is working under very difficult circumstances indeed back home in Greece. But you couldn't see that watching the presidency here, the concentration on the presidency from the Greek government was excellent," he continued.
Samaras, who has been prime minister of Greece since 2012, told the conference, "When the world crisis broke out in 2008 it set into doubt the fundamental values of the European Union. And, I would say, that it was a stress test for the eurozone.
"We are correcting this because Europe has very good reflexes, it can spot and correct errors of yesterday, and Europe can move ahead towards tomorrow" - Antonis Samaras
"It also proved that we have structural weakness, weaknesses of the euro and of the eurozone, and this is exactly what we are fixing now.
"We are correcting this because Europe has very good reflexes, it can spot and correct errors of yesterday, and Europe can move ahead towards tomorrow," he said, adding, "The Hellenic presidency worked on these points."
Speaking on the achievements of the presidency, he highlighted the work done on the banking union and the integrated maritime policy for the union.
"We upgraded in a correct way, in a collective way, problems such as the security of the borders, the migration flows, the legal immigration and in this way we created a new chapter for the union, related more to the seas and the negative and positive aspects of a Europe that has sea all around it.
Samaras explained, "Recently many of the problems were considered as problems which cannot be resolved.
"Now we are moving towards solutions and the Italian presidency, I am certain, are going to continue towards these solutions at a fast pace, solutions that we have already planned."
Comparing today's European parliament to that in which he served in 10 years ago, he observed, "The European Union now is more ready to face and to prevent crisis, and the European Union is more mature now than then."
However, he added, "Of course, we have weaknesses; there is a lot of work to be done."
Referring to the real economy, on which Schulz also raised concerns, he said, "The president of the European parliament is absolutely right when he mentions the problem of the real economy, particularly when he mentions the issue the asphyxiations of the businesses due to lack of cash in the market, and this credit problem is an enormous problem.
He said that in Greece "we see it being resolved slowly by the recapitalisation of the banks and the money that can be given by the new investment entities that are being created.
"From the moment that a decision is made for investment, or some money has been paid, you have a time lag until you can see the positive results of the action and people can feel the positive results in their pockets," he complained.
"But", Samaras concluded, "The problems have gradually set into the proper course, Europe is moving ahead, working properly, and the progress will be increasingly felt by the people of Europe."