Walsh's long-time campaign to expose Armstrong was vindicated when the US Anti-Doping Agency confirmed his drug use late last year, prompting Armstrong to confess to Oprah Winfrey.
Armstrong said in the interview he would consider apologising to Walsh, against whom he had launched a number of personal tirades, particularly after his 2004 book LA Confidential contained allegations about the rider.
Walsh told BBC Radio Five Live's Sportsweek: "I know this is going to sound preposterous but I felt a little but of sympathy for Armstrong.
"Intellectually he had to be remorseful, but emotionally he couldn't do it. Basically, Armstrong knew what he had to do but he wasn't capable of doing it because obviously he's got serious personality issues.
"Lance needed to look remorseful and repentant and you would see a flicker of a smirk crossing his face, and he didn't mean to do that - it was involuntary."
Among the personal attacks aimed by Armstrong at Walsh was the implication that Walsh had a vendetta against the sport since Walsh's son John was knocked off his bicycle and killed at the age of 12.
Walsh described the allegation as "insensitive to the point of evil", and added that while he was not seeking an apology from Armstrong, he would accept it if one was forthcoming.
"I'm not looking for an apology, I don't need one and I don't want one," added Walsh.
"But if he does offer it it will be gratefully accepted.
"I would have lots of questions [for Armstrong]. I would really want to find out what happened to make him the way he turned out to be."
Disgraced former sprinter Ben Johnson said he believed Armstrong faced a tough process following his confession, but would quickly be forgiven by the American public.
Johnson, who was stripped of 100m gold from the 1988 Seoul Olympics after testing positive for anabolic steroids, said he still admired Armstrong in particular for his work with cancer charities.
Johnson told the programme: "The American people will forgive him. I don't think it's going to be a tough time for him to make a living. It's going to be fine for him in a few months.
"The worst thing to happen to him right now is that he's a guy who liked to bully people and be in control and was never wrong, always right.
"That's one of the problems he's going to be facing - his change in attitude, to move forward and tell everyone sorry for what he called them and said about them."