The Portugal international centre-back joined Madrid from Chelsea in the summer and has established himself as one of the best players in the Spanish Primera Division.
The 32-year-old was reportedly on the verge of joining the Blancos from Porto in the summer of 2004 but the move eventually collapsed and he joined the reigning Premier League champions instead.
Now with Madrid and reunited with Jose Mourinho, having worked with his compatriot at Porto and Chelsea, Carvalho believes that he is still in his prime and in a interview with the Guardian said: "I can understand why some criticised the move. I was 32 and I'd been at Chelsea a long time.
“I had a physical problem, which started because I was not given time to recover fully. I was out for longer than is normal for a muscular problem. There was pressure, I wanted to play and I got injured again. It was not properly healed and I had a relapse.
"But I was convinced I'd succeed,” he continued. “I knew I'd play well here. It's a different game and I wanted to prove I was in shape physically and mentally. It would have been easy to stay at Chelsea, where people respected me and moving on meant starting over again.
“But I needed a change, the challenge — and it was Real Madrid. During the last few years at Chelsea I wasn't so happy; I felt saturated. I needed to try something different, get some impetus. I'd become too comfortable. That's not a good thing. I had to show I was still a good player."
Madrid are in the quarter-finals of the Champions League for the first time in seven years and take on Tottenham Hotspur for a place in the last four. On Tuesday evening they host the English side for the first leg at the Bernabeu.
On getting the better of Spurs’ strikers Peter Crouch and Jermain Defoe, Carvalho stated: "They're both very good but very different and we'll be forced to adapt accordingly. Against Crouch we can play higher because he is not so dangerous on the shoulder, while Defoe is quicker behind you.
"I don't mind [whom I have to mark]. I'm not worried about them – so long as I'm fit, strong and playing well."
When asked of a possible confrontation with Chelsea in the final at Wembley in London, the 32-year-old beamed: "Definitely. I talk to the Chelsea players. Whenever they say they've had a bad game, I say: 'Nah, you're strong still.'
"They're the best team in England and I know what it would mean to them to reach the final."
He added: "Chelsea is different, they have ambitions to win it but Madrid have lived it before and want more and more. We have to get into the habit of winning too. It's palpable what this competition represents for Madrid, what success does."
Carvalho reached the final of Europe’s premier club competition with Chelsea in 2008 but lost the match to Manchester United 6-5 on penalties after the match finished 1-1 after extra-time.