FA chairman Greg Dyke and KNVB chief Michael van Praag, who were attending a meeting of the national associations of UEFA in Sao Paulo, which Blatter attended, suggested that the 78-year-old Swiss should reverse his decision to stand for a fifth term in office.
The European executives' attitude toward Blatter was described by one delegate as "a grilling," The Associated Press reported.
Van Praag said that "people link FIFA to corruption and bribery and all kinds of old boy's network" and that a change was necessary to change this perception.
"FIFA has an executive president, and that means you are responsible," the Netherlands federation president said he told Blatter. "People tend not to take you very seriously anymore."
Speaking later to Dutch newspaper Volkskrant, Van Praag added: "The image of FIFA has been tarnished by everything that has happened over the last years. There are very few people who still take FIFA seriously, and whatever way you want to cut and dice it, Blatter is responsible in the end."
UEFA board members lined up later to list grievances with Blatter, including his handling of the 2022 World Cup bidding contest and subsequent issues with Qatar as host plus his criticism of European media for reporting allegations of corruption implicating FIFA officials.
Van Praag stressed that it was not a personal attack on Blatter, who in meetings with Asian and African delegates on Monday accused critics of FIFA's decision to award hosting rights to Qatar of having a racist motivation.
Those comments, in response to claims from the Sunday Times that corruption was central to Qatar's successful bid, were met angrily by FA chairman Dyke, who described them as "totally unacceptable."
"I said to him, 'I regard the comments you made yesterday about allegations in the British media in which you described them as racist as totally unacceptable,'" Dyke said after the meeting. "The allegations being made are nothing to do with the racism. They are allegations about corruption."
Blatter was seeking support from European football's governing body for his re-election bid but failed to find it, with UEFA vice president and former Manchester United CEO David Gill among those unhappy with Blatter's decision to perform a U-turn on his 2011 promise to stand down as president at the end of his fourth term.
"The very fact in 2011 he was clear it was just for four years, that should have been the situation. To change his mind is disappointing," Gill said. "... I think we need to move on. I think we need a full, frank and open debate about what FIFA needs going forward."
Gill echoed the sentiment of Dyke on Blatter's claims of racism, adding: "The statement made by Mr. Blatter yesterday was from our point of view totally incorrect. This was about the issue being raised quite rightly in the British media, which should be addressed by the world governing body, and to try and portray it as racist or a discriminatory attack is totally unacceptable."
The volatile meeting recalled open conflict between Blatter and European football that flared around his original election in 1998 and again for his re-election in 2002 during a financial scandal after FIFA's then-World Cup marketing agency collapsed into bankruptcy and sparked a kickbacks investigation.
UEFA, with 53 of the 209 FIFA members, has a second chance Wednesday to oppose Blatter. That will come in the public arena of the FIFA Congress floor, where he says he will seek acclaim for his expected re-election run.
UEFA president Michel Platini, long seen as Blatter's likely successor, is expected to decide in September if he will challenge his former mentor. Platini did not meet with reporters on Tuesday, though his secretary general, Gianni Infantino, denounced Blatter's description in Sao Paulo this week of a "storm" around world football.
"There is not a storm in football. There is a storm in FIFA, and this storm is not new," Infantino said. "It's something which is coming for years and years and years, and every time it's something else."
UEFA honorary president Lennart Johansson, who lost the 1998 FIFA election in a ballot long dogged by allegations of vote-buying by Blatter supporters, said his old rival should go.
"He has done some good things for FIFA," Johansson said, "but he should stick by what he said [in 2011]."
Still, FIFA members outside Europe show little desire to change a system and leadership that have delivered booming revenues. Blatter told the 11 Oceania countries earlier on Tuesday in a different Sao Paulo hotel that they could expect bonuses from 2014 World Cup revenues higher than four years ago, when each got $550,000.
Oceania leader and FIFA vice president David Chung promised Blatter full support in the presidential ballot scheduled for May 29.
"Rest assured, the 11 members in this room are the first in line," Chung said.