Williams believes Scotland are heading in the right direction

"We are very disappointed, but I couldn't ask much more of my team. They tried their hearts out," he said.

"We missed some tackles and there was naivety at times, but I can't fault them for commitment."

Australia's Stirling Mortlock and Stephen Larkham are out of the game against England next week after suffering serious injuries at Hampden.

Mortlock suffered a depressed fracture of his cheekbone, which Australia coach Eddie Jones said was likely to require surgery, while Larkham was left with a broken forearm.

It's a great pat on the back to this team to come this far in such a short period. Matt Williams

Jones added that winger Clyde Rathbone only had a 10% chance of playing at Twickenham as a result of a groin injury which saw him replaced just before half-time.

"We are going to need all hands on deck next week," Jones said.

But he added that he was delighted to get back to winning ways following last week's defeat at the hands of France.

"It was a much improved performance from our previous Test," he said.

"I thought we were a bit loose in our ruck defence and finishing some movements off, but we have to learn in these conditions so it was a great experience.

"It was a pretty tough game and Scotland played very well and certainly we've got plenty of work to do."

Scotland collected the wooden spoon in last season's Six Nations and have only beaten Samoa and Japan in their last 13 matches.