All three of the England youth internationals made notable contributions to Southampton's Barclays Premier League opening-day triumph having been named in the first XI, with defender Shaw earning the penalty, via a challenge by Youssouf Mulumbu, from which Rickie Lambert scored the winning goal in the 90th minute.
And asked about Shaw, his fellow full-back Chambers - who was making his first senior start - and midfielder Ward-Prowse, Pochettino said: "All I can say is that I am confident that they are good enough players to play in this league.
"I am only taking advantage of the work that has been in place already at Southampton for the last four years - the amazing work that (executive chairman) Nicola Cortese has done in that sense, in bringing young players through the academy system."
Two other players who made a positive impression within the Southampton side on Saturday were the pair of new signings Pochettino made over the summer, defender Dejan Lovren and midfielder Victor Wanyama.
Pochettino believes those additions have enhanced his team's competitive edge, and he has indicated there could be further new arrivals before the end of the transfer window.
The Argentinian said: "I think that is exactly what the new signings have come in for - to improve the team where I thought it needed improving in our defence and the midfield.
"As opposed to last season, we are a much more competitiveteam now with these two new signings.
"We are still looking in these last two weeks of the transfer window, and we'll see what happens."