"Argentina were very good up front, as expected, but we settled into the game well, especially after the early try for Matthew (Morgan).
"We now have to continue to train hard before playing New Zealand on Tuesday. There are some things we need to sort out before then - it is sure to be the hardest game of our lives - but if we keep working hard we can hopefully we can put in another good performance and do well.
"A lot of players have played in this tournament and gone onto bigger and better things, such as Wales internationals Sam Warburton, Leigh Halfpenny and Jonathan Davies. I don't see any reason why players in this side can't do the same thing."
Cook's thoughts were echoed by coach Rob Appleyard who was pleased to kick the tournament off with a victory.
Appleyard said: "For the first game of the tournament, it was a good outcome. A lot of the players hadn't played competitive rugby for a while so it was good to get the game legs going.
"There were elements of the performance that were very good but I felt we were also a little inconsistent at times.
"We didn't come here just to beat Argentina, we came to be successful in the competition so it's a great first step but there's a lot more to do. We're going to go back and be quite critical because New Zealand is a much sterner test for us and we need to tighten up on the errors we made.
"If you want to do well in any competition, you have to do well against the best teams. It will be a high-paced, physical game on Tuesday, New Zealand are a formidable force but we have to match that. We showed against Argentina that our backline functioned well, with Matthew Morgan and other backs making scything breaks, but our forwards fronted up too and our defence stood up well so we've just got to make sure we bring that physicality to the table now when the stakes are higher against New Zealand."
Meanwhile, Wales Under 20 hooker Sam Parry returns home from the Junior World Championship in Italy this weekend after being diagnosed with mumps earlier in the week. He has been confined to isolation for the past few days before being authorised to fly home tomorrow (Sunday). He will be replaced in the 26-man squad by Cross Keys and Dragons academy hooker Jamie Sollis.