Speaking at a news conference in Strasbourg on Tuesday, Philippe Lamberts, co leader of the Greens/EFA group, suggested that Barroso had acted with "indecent" haste in taking up the job less than two years after he stepped down as Commission President.
Lamberts joined others in calling for an extension of the "cooling off" period from when a European Commissioner steps down and then takes up another job.
Commissioners are governed by a code of conduct requiring them to seek permission before taking jobs for up to 18 months after stepping down.
RELATED CONTENT
Lamberts added, "You can never prevent people from not behaving decently and moving to a company like Goldman Sachs, with its connections to the Eurozone crisis, borders on a question of decency.
"We need an extension of the cooling off period before a Commissioner can take up another post in the private sector, but must also be careful not to tar everyone with the same brush. Let's remember that the relationship between French policymakers and French banks is almost incestuous."
Further condemnation came from Dutch GUE/NGL group member Dennis de Jong, who cited recent reports that Barroso had had close contacts with Goldman Sachs during his time as President.
Addressing a separate press conference, De Jong said, "Barroso has admitted he had these contacts during his term. This shows he didn't have a clue about the principles of integrity and discretion to which he was supposed to adhere.
"If he did not think there was a problem with such meetings, then there is something wrong with him."
He added, "What this shows is that we need clearer rules and guidelines on issues of integrity and discretion because it is clear some people don't know what that means."
The Commission has opened an ethics investigation into the Barroso case. If a breach of its ethical code is proven, it can deprive a former Commissioner of his/her EU pension.
The Commission is also scrutinising former competition Commissioner Neelie Kroes over her directorship at a company in the Bahamas. Kroes, who was EU competition chief from 2004-2009, failed to declare the corporate role to the Commission as required under ethics rules.
De Jong said, "I think we can safely conclude that the Barroso Commission was a big mess because there is a long list of former Commissioners, including Kroes, who took up posts with big business or financial institutions soon after stepping down.
"The whole system is not right and the ethics committee itself needs looking at and its mandate broadened."
Further comment on the so-called "revolving doors" involving former Commissioners came from Socialist leader Gianni Pittella, who said he also supports an extension to the cooling off period.
The Italian MEP said, "Binding restrictions on when a former Commissioner can take up a new position are needed. And we also need to ensure that these are respected."
ALDE group leader Guy Verhofstadt also supports "strengthened" rules but argued that the Commission should be allowed to carry out its inquiry into the Barroso case.
The Brussels executive has been urged to bolster its transparency rules after drawing criticism amid the ethics inquiries into former officials, including Barroso.
Press reports this week suggest that Goldman Sachs officials, including CEO LLoyd Blankfein, held meetings with Barroso while he was leading the Commission that were not disclosed publicly at the time.
Barroso, who waited the required 18 months before taking up a corporate post, has criticised what he calls "discrimination" against him in the case, saying he "scrupulously observed" all the rules.
He is advising Goldman Sachs on Brexit and other global issues in his role as non-executive chairman of the firm's international unit.