Thomas, who chaired the RFU for five years, added his voice to that chorus when he said England would still be vying for a place in the final if they had reappointed former England coach Clive Woodward.
"Before I left, I warned the RFU board that Stuart was not the right man for the job," Thomas told Wednesday's Daily Telegraph.
"He had not played or coached the game at the top level and does not have the technical experience or expertise to cut it at international level.
"Look at the coaches in the quarter finals of the World Cup -- Warren Gatland, Michael Cheika, Steve Hansen and so on -- they are proven at the very highest level and they have an X-factor.
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"The brutal truth is that Stuart does not have that at the moment. We have gone nowhere during the last four years and that is a terrible indictment."
The hosts crashed out in the pool stages after back-to-back defeats by Wales and Australia.
The future of Lancaster, who has a contract until 2020, has been hotly debated and he could still lose his job after a review of the campaign headed up by RFU Chief Executive Ian Ritchie.
"The overriding emotion for me has been one of profound frustration at a lost opportunity," Thomas told Wednesday's Daily Telegraph.
"I am not going to see another home World Cup in this country again and an awful lot of other rugby fans won't either. The country got behind the team massively, but I'm sad to say they were let down."
The RFU named Lancaster interim England coach, succeeding Martin Johnson, a month after Thomas left the body in acrimonious circumstances at the end of November 2011.
Thomas said TV pundit Woodward, who steered England to their only World Cup triumph in 2003, was a resource English rugby could not afford to waste.
"The tragedy is that Clive should be managing English rugby," Thomas added.
"If he was, I am convinced we wouldn't be in the terrible mess we are now. We would be contending to win the World Cup, not packing our bags.
"It was painful to see someone who should be in charge of English rugby sat in a TV studio."
(Reporting by Simon Jennings in Bengaluru, editing by Nick Mulvenney)
