Rodri fired in from a Bernardo Silva cutback midway through the second half at the Ataturk Olympic Stadium to decide a game in which City were knocked out of their usual rhythm and lost Kevin De Bruyne to injury.
Erling Haaland, scorer of 52 goals this season, went a fifth straight match without finding the net, but City had enough to edge out opponents who had never been expected to get this far.
"It wasn't easy. What a team we faced, unbelievable," Rodri told British broadcaster BT Sport.
Having already claimed a fifth Premier League title in six seasons, and added the FA Cup, City are the first English club to win such a treble since Manchester United in 1999.
That same month 24 years ago, City won the English third-tier play-off final on penalties against Gillingham.
Now they have established themselves as England's dominant side and have finally added the biggest prize in European club football, two years after losing to Chelsea in their first final.
"I think we made history. The good thing is that we want more. This project is to want more, more ambition," Rodri added.
The match was watched by owner Sheikh Mansour, who made a very rare appearance at a City game as his team capped their rise from also-rans to superpower in the years since he bought the club in 2008.