The Spanish midfielder beat home winners City as they beat Inter Milan 1-0 in the Champions League final to complete the treble in Istanbul on Saturday.
The 26-year-old now hopes City can build on a first European crown and create a long-lasting dynasty.
Rodri, who has developed into one of the world’s best midfielders since his £62.8m move from Atletico Madrid four years ago, said: “From my point of view I want to thank the team. It is the victory of many years of work at this wonderful club.
“They trusted me to come here, even though the change was not easy. It was a new culture for me and now I arrive with the most important goal in the history of this club.
“We deserve it. What a season. we deserve it.
“I said it before the game that it is so important to win against Inter because we can build a legacy for the future. That’s what teams like Real Madrid, Bayern Munich, Barcelona, AC Milan – these kinds of clubs – have done in the past.
“We believe we can do it again.” I think that’s why it’s so important.”
City were not at their best at the Atatürk Olympic Stadium.
With Inter proving their dogged opponents, City could not replicate the enthralling football recently swept by Arsenal and Real Madrid, nor the control they displayed over Manchester United in the FA Cup final.
Instead, they relied on their character and quality and Rodri finally got the ball rolling in the 68th minute with a controlled strike from the penalty spot.
Rodri said: “I think that was the only time I went forward in the game because Inter were so narrow and I wanted to make sure the two strikers were not comfortable.
“At that moment I just saw the space. At first I thought about shooting hard, but then I realized there were six or seven players in the goal area and I thought, ‘No, I’ll put it on the first post’.
“The end result was unbelievable but with half an hour to go it was a great effort from all of us.
The goal capped a memorable season in which City retained the Premier League – their fifth title success in six years – and beat arch-rivals United at Wembley to lift the FA Cup.
They are only the second side to win all three of these trophies in the same season, emulating United’s achievement in 1999.
Their success was relished by owner Sheikh Mansour, who traveled to Turkey to watch City play in person for only the second time since buying the club in 2008.
Sheik’s support has taken City from mid-table in the Premier League to the top of the European game and Rodri wanted to pay tribute to the players who paved the way for their success.
He said: “When I finished the game, I don’t want to forget players like Fernandinho, Sergio (Aguero), David Silva, (Vincent) Kompany – many players who worked eight, nine, 10 years at this club to help. gets to this level.
“We are reaping the fruits (of their labor) and this victory is for all of them.”
City party overnight at their hotel in Istanbul before heading home on Sunday afternoon. They were flown back to Manchester on a Boeing 787-9 Dreamliner in club colours.
The celebrations will continue on Monday with an open-top bus parade through Manchester city centre.