Conte led an unfancied Italy side to the quarter-finals of Euro 2016, eliminating defending champions Spain in the last-16 and drawing praise for his tactics.
The coach announced his intention to step down in the months leading up to the tournament, joining Chelsea following the campaign in France.
Gian Piero Ventura subsequently took the helm but failed to guide the Azzurri past Sweden in a play-off for a spot at Russia 2018, with Tavecchio standing down in the aftermath.
Asked what his greatest regret from his time at the FIGC helm was, Tavecchio told La Gazzetta dello Sport: “I did not give Conte the extra €2.5million he wanted. I would have got it back with three friendlies.
“Antonio was on €4million and he asked for €6.5million. He would have stayed with the Azzurri and we would be in Russia today.
“But is it right to give what we were investing in the youth sector to just one man?”
Sweden beat Mexico 3-0 to win Group F in Russia, with defending champions Germany suffering a humiliating exit.
Tavecchio claims many have underestimated Janne Andersson’s side, who will face Switzerland in the last 16 in St Petersburg on Tuesday.
He said: “They have given us a great excuse – too many have underestimated them.
“I’ve repeated it since the draw that it did not go well. They called me mad and said Greece would’ve been worse.”