"You've got to give Portugal their due, they didn't lie down, they worked hard and got a try from one of our own mistakes, but they'll take away some good things from the game," said Walton.
"Our boys are lucky in terms of their conditioning, and they're going into professional contracts whereas not many of the Portugal boys have that opportunity.
"We played Scotland three weeks ago and we beat them quite convincingly, and that will be the toughest thing, we need to make sure we get the same result again but we need to work hard and improve on the things that didn't go so well against Portugal. The Scots will improve and be a better team this time.
"I'm very happy, it's a good start, we put a lot of points on the board but there's a lot to work on. When we watch the video there will be a lot of mistakes that we have made that we have got to improve on."
Scotland progressed after a far tighter contest against Wales in Moirans - eventually triumphing 18-17.
Morgan Tyler, Tom Phillips and Michael Snook tries had put Wales into a commanding 17-3 lead but two tries from Angus Rennie and the boot of full-back Gavin Lowe saw them home.
Elsewhere France beat Italy 32-0 and Ireland edged past Georgia 31-27 to seal their progression to the semi-finals.