Noel Mooney, chief executive of the Football Association of Wales (FAW), believes Fifa made a mistake by not barring Russia from all international football sooner.
Last week, Russian President Vladimir Putin started a military invasion of neighboring Ukraine.
Fifa initially did not issue a ban, which it later reversed, by which time Wales had announced their refusal to play any games against Russia.
"Their initial decision was not a good look," Mooney told BBC Walescast.
Wales, England, Poland, the Czech Republic, and Sweden were among the first to reject to play games against Russia.
That decision was made when Fifa instructed Russia to play their forthcoming games in neutral territory under the name Football Union of Russia, without their flag or anthem.
Fifa and Uefa have since suspended Russian football clubs and national teams from all competitions.
Fifa's initial decision was based on the International Olympic Committee's (IOC) approach, which penalized Russia for state-sponsored doping with a partial Olympic ban - of its anthems, flags, and official team name - but still allowed the country's athletes to compete.
Mooney was dismayed when he saw how Fifa planned to handle the problem at first.
"Fifa's [first] decision was to stick with the old IOC concept," Mooney explained.
"'My lord,' I exclaimed as I saw the news on my phone.
"When the IOC came up with those anti-doping ideas, it was completely different; this is terror, and it is far beyond the pale.
"When I saw Fifa's judgment, I knew it would not stand up in court, and at the FAW, we have to make our own decisions because we have our own social conscience.
"When Fifa's statement was released, we knew it wouldn't cut it and would rapidly be viewed as inappropriate.
"Thankfully, they swiftly reversed that, but their initial decision was not a good look."
