The 1970s star and surgeon spoke as researchers found a link between repeat rugby concussions and reduced blood and oxygen flow to the brain in later life.
The study said it may show why memory, thought processes and co-ordination declined in some ex-players tested.
World Rugby has said it welcomes new research into players' welfare.
Williams, a British and Irish Lion renowned for his toughness on the field in the Welsh game's 1970s golden era, said governing bodies must take more notice of research.
"There is no doubt the generations after us are going to be left worse off than we were," said Williams, 74.
Commenting on the findings of the study, in which he was involved, he said: "I'm not pleased, but it backs up what we felt was the problem."
A separate legal case is ongoing where former players are suing the WRU, RFU and World Rugby, previously known as the International Rugby Board.
The players say they sustained permanent brain injuries in the game.
The case will be decided by a judge based on the evidence presented in court.
Thomas Owens, co-lead investigator on the University of South Wales (USW) study, said research found that retired players with a history of concussion had mild cognitive impairment.
"This is a state whereby the cognitive function of these individuals, in term of the way someone thinks, remembers information, processes that information and co-ordinates the body's movements declines over time, and particularly throughout ageing".
He said this put them at "increased risk of developing neurodegenerative diseases later in life".
But the researchers said not everyone who played contact sports would go on to develop cognitive decline.
Williams said he had no concerns for his health but his generation was worried about neurodegenerative diseases.
He is particularly concerned about the generations that came after him, especially given the intensity of the game now.
Williams said: "I had been an orthopaedic surgeon for 35 years. I thought it was good to get involved because of the concern about lots of sports having problems with concussion".
He cited "serious worries, particularly with the laws of the game now, where they stand right on top of each other".
"There seems to be a bit of a conflict between the laws, and the early onset of cognitive degeneration," he said.
He said cognitive health was not really known about when he played, but much less time was spent training.
"The game was amateur, we only probably had physical contact once a week. Now they have it every day, the brain needs time to recover, it's like any organ in the body, it is quite a worry, it's repetitive, not even huge bangs but repetitive small injuries to the brain can be a problem in later life."
The 55-cap full-back wants the game to return to how it was in the 1970s, with more space for players, "to decrease the ferocity of the hits". He also wants reduced tackling and contact in training.
He urged governing bodies "to take more notice than they do" of studies such as this.
Williams reflected on an infamous moment of his career when he was stamped on by New Zealand prop John Ashworth while playing for Bridgend against the All Blacks in 1978.
Knowing what he knows now, he probably would not have returned to the field after having his face stitched up by his father at the side of the pitch.
Scientists at USW's neurovascular research laboratory analysed the brain health of 20 retired players aged between 60 and 80 who had suffered concussions.
For the first time, researchers found they had reduced blood and oxygen flow to the brain due to less nitric oxide, which helps blood vessels regulate blood around the body.
Some exhibited signs of mild cognitive impairment and all were outperformed by the control group in cognitive function tests.
The researchers said this was the first study to determine mechanisms that may cause cognitive decline and has implications for other contact sports.
It is hoped the research may contribute to improving protection for players and help with the introduction of pitch-side blood or saliva tests for concussion.
Mr Owens said: "It's important to note that we don't want to stop players playing rugby, but we want to make them inherently aware of the risks associated with forms of brain trauma and concussion.
"Make them aware, improve the way that we detect concussion at the pitchside and then improve the way we care for players following retirement."
Former Bridgend RFC captain Meredydd James also took part in the study, and said there was no knowledge about the dangers of concussion in his era, but he started to feel the effects later in life.
"Initially you have some aches and pains, I used to have a bit of back trouble," he said.
"I think for the first 20, 30 years you just go along with it and you can't say it was definitely related to rugby.
"But I think when you get to 55-plus, a little bit of memory loss, perhaps the recall, perhaps balance, those are some things starting to kick in, and you think: 'Concussion, dementia could it be something like that'?"
There are other studies taking place investigating the health of former players. Lifestyle changes, including poor diet, alcohol dependency and lack of exercise may also accelerate the cognitive decline of former athletes.
USW researchers said they recognised this study had limitations in the relatively small sample size and it relies on participants remembering past concussions.
But they are aiming to carry out a larger study and investigate the potential differences in brain health between male and female athletes in contact sports.
World Rugby previously said it "welcomes all research that can inform and support our recently launched strategy to cement rugby as the most progressive sport on player welfare" and undertook "a wide-ranging evaluation of contact training".
In 2021 it said: "It is at the heart of everything that we say and do as a sport. World Rugby recently committed to double our investment in player welfare and new concussion research and initiatives."
The WRU has been asked to comment.