South Africa looked set to force extra time after producing a disciplined defensive display to frustrate the tournament co-hosts. However, Stephen Eustaquio broke Bafana hearts in the 92nd minute, firing past Williams to end their historic World Cup campaign.
Despite the disappointment, Bafana returned home on Thursday with plenty to be proud of after becoming the first South African national team to reach the knockout stages of a FIFA World Cup.
"It's obviously very disappointing to concede so late in the game," Williams said upon the team's arrival.
"That's a critical phase, and that's when you need to focus even more. It always hurts more to concede when there are only two minutes to go. But you could see the guys were exhausted. There were a lot of heavy legs out there.
"It was like a sucker punch. It came at a time where we didn't have enough left in the tank to get the goal back and chase the game. There simply wasn't enough time left to launch a comeback."
The captain believes the heartbreaking defeat will ultimately help Hugo Broos' young squad mature as they continue their upward trajectory.
"Like the coaches mentioned, there are a lot of lessons we'll take from this tournament. I think almost all the goals we conceded came during critical phases - either at the very beginning of the match or right towards the end," he added.
"Those are the moments where you really need to be switched on and fully focused. That's the biggest lesson we'll take away, and it's one that will help us grow as a team going forward."
While the late defeat against Canada brought Bafana's remarkable World Cup journey to a cruel end, Williams believes the experience gained on football's biggest stage will strengthen the squad as they prepare for future international competitions.
South Africa's historic FIFA World Cup campaign has reignited the debate over the future of Bafana Bafana coach Hugo Broos, but Sports Minister Gayton McKenzie believes the Belgian has already done enough to be immortalised.
Portugal head coach Roberto Martinez said his side were ready to begin what he described as a "second World Cup" as they prepared to face Croatia in the Round of 32 in Toronto on Thursday.
Oswin Appollis' absence from Bafana Bafana's return to South Africa has intensified speculation that the Orlando Pirates winger could be on the verge of securing an overseas move.
Norway manager Stale Solbakken has insisted his team had nothing but respect for Brazil coach Carlo Ancelotti ahead of their FIFA World Cup last-16 meeting, explaining that a viral dressing-room video was never intended to provoke the Italian.
