But Williams insists the optimists north of the border have to take a reality check by comparing how far the Italians have progressed in recent years and how far the Scots have regressed.
He said: "The days of treating the Italians as easy beats are well over. In the world rankings we are ninth and they are 10th, so they're coming after us.
"We're 12 players down from the last World Cup - so to expect us to win is not realistic. To go there and say we will win is not on."
Williams is hardly about to get carried away with his team's apparently slightly improved showing against world champions England, following their trouncing by Wales.
"Scottish rugby is in serious trouble, and we are a long way behind because we haven't had the resources," he said.
"When I took the job I realised it would be 12 months of difficult games. I said to them if they wanted me just to come in and win the next three games then they had the wrong guy - I wanted to be winning in 18 months time."
One of Williams' first tasks, he believes, is to instil the right attitude in his charges.
"Of course we want to win every game - but wanting to win and deserving to win are two separate issues," he said.
"You don't win international games by accident. We've got to get to that level where we deserve to win games - but to get to that level will take time.
"We've got to take a longer term view and we've got to educate the players for the next World Cup in four years time."