The Swansea City defender played a crucial part in his side’s stunning adventures in the European Championships in France, which saw Wales end a 58-year wait to reach the finals of a major tournament.
Chris Coleman’s charges surprised as they went all the way to the semi-finals after topping a group including England and Russia.
Portugal eventually ended their run with a 2-0 win but Williams feels that won't hinder their progress.
"We've said to ourselves on the bus: 'imagine if we had won the tournament'. Because looking at the streets, it feels like we have," said the 31-year-old as the team were paraded around Cardiff on their return home.
"After the Russia World Cup hopefully it will be the same again, but with a trophy."
Liverpool midfielder Joe Allen echoed the sentiments of his team mate, insisting Euro 2016 campaign has to become the benchmark.
"We can keep this momentum going," he said.
"We are all very proud of what we have done and hope this is the benchmark and that we can look forward to more future success."