Hingis, 37, called time on her career, which spanned three decades, for a third time on Thursday. Federer, who won the 2001 Hopman Cup alongside Hingis, said he heard at the start of the year and again last week that Hingis intended to call it quits for good at the end of the ongoing WTA Finals in Singapore, where she has reached the doubles semi-finals.
"Martina was partially the one who showed me how it was all done," said 19-time Grand Slam champion Federer.
"It was great for Switzerland to have someone of her calibre. We were very lucky. I loved playing with her at the Hopman Cup, she was always super friendly, I love that about her.
"I'm not sad to see her retire, she's been in the game for long enough, she seems at peace with her decision -- that's wonderful. I've always been a fan of her and I always will be."
Hingis announced her "definite" retirement earlier on Thursday, signalling the end of a career which took her from 1990s teenage superstar to doubles world number one some 20 years later.
"I think now it's definite. It's different, because before I walked away thinking I might come back," Hingis told reporters after her 6-3, 6-2 doubles win alongside Chan Yung-Jan over Anna-Lena Groenefeld and Kveta Peschke in Singapore.
"After a season like this, I think it's also perfect timing. You know, you want to stop on top and not when you're already going backwards. I couldn't ask for a better finish."
Hingis had five Grand Slam singles titles to her name when injuries drove her into her first retirement in 2003, when she was just 22.
She returned two years later but the comeback was short-lived and Hingis stepped away from the sport again after failing a drugs test at Wimbledon in 2007.
But she has enjoyed considerable success since her reincarnation as a doubles specialist, and ends her career at the top of the rankings and with 20 major titles in doubles and mixed doubles.