Speaking in Parliament on Tuesday, Juncker reiterated his determination to crack down on the problem which has been highlighted by a series of scandals such as the Panama Papers revelations.
But, regarding his own culpability as a former finance chief in Luxembourg, he told MEPs, "You have to realise that the world was a very different place back then."
Juncker was appearing before the European Parliament's committee of inquiry into money laundering, tax avoidance and tax evasion (PANA), with MEPs demanding answers as to what role he personally played in the overseeing the Grand Duchy's development into one of the world's biggest tax havens.
In his opening remarks, Juncker was keen to outline what the Commission was currently doing to tackle the issue, saying it had introduced 12 separate items of anti-tax avoidance legislation in the past year, with another proposal set to be tabled shortly.
He said citizens' trust has been seriously shaken by the Panama Papers affair and other revelations about how large companies had sought to avoid their tax obligations.
Juncker said that some €70bn had been lost to public coffers through tax avoidance and evasion. The tax burden was 30 per cent heavier for individuals, he said, than some multinationals, a situation he described as intolerable.
The Commission, though, had taken action to address those companies that tried to gain an unfair advantage and Juncker said some of the measures taken had achieved remarkable results.
He told the hearing, "We have adopted ambitious reforms and these steps seek to unravel the schemes used by some companies. All this information is available to the public."
Future measures include legislation on cross border VAT fraud, money laundering and providing greater protection for whistleblowers, he said.
The Commission will also come forward with a new, expanded version of its blacklist of tax havens by the end of the year, he said, although this will not contain the names of any EU member states.
"These are unprecedented advances in the fight against tax evasion but we want to go further still because we are still only in the early stages. We are counting on the Parliament's support in this."
He added, "The various tax avoidance scandals have actually made our task easier but the pressure must not let up and we need an energetic response to this issue."
However, Juncker admitted that the Commission lacked the necessary resources to follow up disclosures about all tax havens and tax irregularities.
He said, "We do not have the resources of some of the political groups and therefore rely on the goodwill of member states in providing information on these things."
Committee Chair Werner Langen told Juncker that the aim of the hearing was not to apportion blame, but to find ways of addressing the tax issue.
However, he said he and his colleagues had been disappointed by the "general refusal of people, including bankers and lawyers and previously exposed individuals" to appear before the committee.
Fabio De Masi, a Vice-Chair of the committee, said, "As Luxembourg's Prime Minister from 1995 to 2013, Juncker took on the role as architect and godfather of one of Europe's biggest tax cartels.
"And yet, he wants to wash his hands and proclaim innocence. He claims never to have negotiated any tax deals with multinationals as this was always done by the tax administration.
"Juncker embodies a European Union that serves the multinational corporations; he is therefore part of the problem - not the solution.
"Instead of hiding behind tax officials, Juncker should come clean about his past. As President of the Commission, he must make it clear to Luxembourg and other EU tax havens that they can no longer block meaningful progress in the fight against tax dumping or their cooperation with the PANA committee."
More criticism of Juncker came from German MEP Michael Theurer, who told Juncker, "I find your response today to be very disappointing. This has been a missed opportunity."
Another German committee member, Peter Simon, told Juncker that for many people he was still directly linked to a country - Luxembourg - which had adopted a tax system designed to "get rich via tax evasion."