Thatcher supported a ban placed on English teams by UEFA following the Heysel Stadium disaster in 1985, and Nicol blamed the former Prime Minister, who died on Monday, for causing the game to regress in the aftermath of the tragedy.
"She personally had a huge impact on the whole of English football and not for the good," Nicol told ESPN.
"She was responsible for robbing a generation of football players from playing in European football and she robbed a generation of fans of seeing the best teams and players as well."
The Scot also mused on how Thatcher had affected his own career personally, saying that he missed out on a trio of European campaigns himself because of the-then Tory PM.
"Purely from a personal point of view, she robbed me of the chance of playing in three European Cups," he said.
"Before [Heysel] I'd played in two [with Liverpool] but then we were withdrawn from European football on her say."
Nicol played for the Reds from 1981 to 1995, making over 300 appearances during his time at Anfield.