Sanchez scored only three Premier League goals in 32 appearances after signing for United from Arsenal in 2018.
The Chile international saw his unhappy spell at Old Trafford come to an end when he was allowed to join Inter on a season-long loan.
Sanchez has reunited with ex-United striker Romelu Lukaku at San Siro and he feels coach Antonio Conte's desire has helped him to settle in Milan.
"It was a bit like falling in love with football again," Sanchez told UEFA.
"I already knew the coach and some players, and I think the club is preparing something nice for the future.
"If I'm not mistaken, Inter haven't won anything for seven or eight years.
"Yes, it was a bit like finding love for football, together with the desire to win something with this club.
"I believe the coach wants to win everything. You can see it from how we train and how we play games. He conveys his desire to the players and is positive for both the club and the team in general."
Inter could only draw at home to Slavia Prague in their Group F opener while Barca were held to a draw away to Borussia Dortmund.
"When I arrived, there was talk that it might be the best Barcelona [team] in history," Sanchez, who won La Liga in 2012-13, said.
"There were [Pep] Guardiola, [Lionel] Messi, Xavi, [Andres] Iniesta and [Carles] Puyol, who is the best captain I've ever known in my career.
"It was great. Barcelona taught me a different style of play, based on ball possession. Plus, I had team-mates you could give the ball to, knowing that then they would give it back to you perfectly.
"If you train with such strong players you can only improve. I try to improve myself every day and this helped me grow as a player.
"At Barcelona I learned a lot, in the sense that I grew up. There were great players who had won the World Cup and they allowed me to improve day after day, even physically."