World number one Federer beat Roddick three times in the Wimbledon final in 2004, 2005 and 2009 with their last encounter decided 16-14 in the final set.
“He could have gotten that title,” said Federer, whose stranglehold over Roddick also extended to the 2006 US Open championship match.
“That’s what I said about him in 2009. He deserves this title as well. In my mind, he is a Wimbledon champion, a wonderful ambassador for the game.
“I am thankful for everything he has done in the sport here in America. It’s not been easy after (Andre) Agassi, (Pete) Sampras, (Jim) Courier, (Michael) Chang, (Jimmy) Connors, (John) McEnroe, you name them.
“It’s been hard for him at times but I thought he always did the best he could. That’s all you can ask for from a guy like Andy.”
Roddick, the 2003 US Open champion and a former world number one, turned 30 on Thursday and marked the occasion by revealing his intention to retire once this US Open is finished.
“It’s sad. That’s how I felt when Andy told me,” added Federer.
Serena Williams, a 14-time Grand Slam title winner and a fellow 30-year-old, said she had known for a while that Roddick was going to quit.
“He told me a while ago, last year, that this would be it. He told me again when I was at his house in Austin at the end of the year,” said Williams, a triple US Open champion who won her 60th match at the tournament on Thursday.
“I was thinking, ‘Please change your mind.’ It’s tough when you don’t want to go out there and do the work to get ready and the preparation.
“Ever since I have been on tour, it feels like Andy has been there. He has been great for American tennis, great for the US Open, doing so much, playing so well, just being such a great player.
“He has a great attitude and a lot of people look up to him. It’s incredibly sad for me to lose a friend on tour. It’s going to be hard.”
Not everything is bleak for American men’s tennis despite Roddick being the last man from the country to win a major.
There are four US men already in the third round with another seven having the opportunity to join them on Friday when the second round wraps up.
James Blake, at 32, one of those men in the third round, said he had half-expected Roddick to carry on especially after his title win in Eastbourne on the eve of Wimbledon and his defeat of Federer at the Miami Masters.
“That showed that he could still beat the top guys,” said Blake.
“But I also knew that his body wasn’t the same. I don’t even know what it feels like but it’s got to hurt to serve at 140mph for 10, 20 years.
“I know he’s always icing his back, his knees and his shoulders can be problematic.”
Venus Williams, a seven-time major winner, said she was not ready to follow Roddick out of the sport despite suffering a second round loss to Angelique Kerber on Thursday.
“When you are ready, you are ready,” said Williams. “He’s a great American champion and I will miss him.
“If I was getting killed out there by my opponents, then I would think it was time to hang it up. But I am killing myself at the moment.”