France international Fekir appeared certain to join the Premier League club ahead of the 2018 FIFA World Cup.
The attacker underwent a medical but Liverpool backed out at the last moment, reportedly due to concerns over knee problems dating back to 2015.
Fekir's former agent, Jean-Pierre Bernes, described the knee issue as "part" of the reason the move collapsed.
The pair ended their professional relationship in April.
"Lots of lies were told and that affected me," Fekir told L'Equipe.
"Especially those claimed about my family. It hurt both them and me. Especially when you know that what's being said is false.
"When you are a good person in life you always end up being happy and at peace, and today I am happy and at peace. Others are not, but let's not go into detail.
"My knee is good. I had a quick medical check at Clairefontaine, my knee wasn't even mentioned.
"If my knee had been in such a bad state, why would [Lyon president Jean-Michel] Aulas have made an offer [of a new contract]?"
Fekir said: "You want the truth? Even I don't know, I assure you!
"I did my medical and then [Liverpool] decided not to sign me. At some point they wanted to have me believe it was because of my knee, but an excuse needed to be found because the medical tests that I did at Clairefontaine were very clear.
"My knee is perfectly fine and I feel fine. There are no issues at all with my knee."
Fekir spent the 2018-2019 season at Lyon before leaving for LaLiga side Real Betis, for whom he has scored two goals in three games.