Nikita Simonyan, the former Soviet Union striker and coach, made his comments following another episode of fan violence in Russia last month, during the Russian Cup match between Spartak Moscow and Shinnik Yaroslavl.
"As you remember, English clubs were banned from European competitions for five years (in the 1980s)," Simonyan told a news conference.
"But the measures taken by Mrs Thatcher led to jail terms and stadium bans for football hooligans, and everything has calmed down in England."
English football was bedeviled by hooliganism in the 1970s and 80s. A riot at the FA Cup game between Luton Town and Millwall at Kenilworth Road in 1985 led to a controversial national debate on the issue led by Thatcher.
The then prime minister and Conservative Party leader backed an ultimately unsuccessful bid to make football supporters in England carry identity cards.
It was the Hillsborough tragedy of 1989, when 96 Liverpool fans died at the FA Cup semi-final between their team and Nottingham Forest - that had the most profound effect on how football is watched in England.
The independent inquiry into the disaster culminated in the Taylor report, a document sent to Thatcher's government in January 1990 that concluded that the "main reason for the disaster was the failure of police control".
It recommended several measures designed to improve fan safety at sporting events, the most dramatic of which was the introduction of all-seater stadiums to England's major football clubs.
In September 2012, the Hillsborough Independent Panel said no Liverpool fans were responsible for the deaths.
Spartak Moscow and Shinnik Yaroslavl have been fined and ordered to play matches behind closed doors following the crowd trouble at their match at the end of October.
Earlier that month, a section of CSKA Moscow fans had racially abused Manchester City's Ivory Coast midfielder Yaya Toure, prompting a UEFA fine and a closure of part of their stadium for their next Champions League match.
Russia coach Fabio Capello last week urged football authorities in the country to step up their efforts to curb racism in the sport, saying "they should try to isolate them from football".
Simonyan, the 87-year-old who was part of the Soviet Union's first World Cup finals in 1958, added: "I've spent 68 years in football and I'm with both hands for the measures taken by Thatcher."
Earlier this month, the Serbian government's secretary of sport, Nenad Borovcanin, said the Balkan country must emulate Britain in preventing football hooliganism after another Belgrade derby was marred by fan violence.
Crowd violence and racism could prove embarrassing for Russian President Vladimir Putin, who faces ethnic tensions in Russia as it prepares to host the 2014 Winter Olympics in February and the 2018 football World Cup.
(Writing by Angel Krasimirov, editing by Stephen Wood)
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