The highly-rated 18-year-old was handed his senior debut in Wednesday's 1-0 friendly defeat of Denmark at Wembley, just 16 months on from making his Barclays Premier League bow.
Shaw replaced boyhood idol Ashley Cole at half-time and slotted in seamlessly at left-back, providing Hodgson with a pleasant selection headache when it comes to choosing his squad for Brazil.
Leighton Baines' place is all but assured, so it looks to be a straight fight between Shaw and experienced Chelsea defender Cole for the other left-back berth.
"I think Roy Hodgson has a very big problem on his hands," Pochettino said of England's selection dilemma.
"I don't know what is going through Roy's mind at the moment regarding Luke Shaw but in light of the 45 minutes he played he showed he deserves to be in the team and has the quality to be in the team.
"I thought it was an amazing moment for him, for Southampton Football Club in general and especially for all the managers and directors he's had in the academy.
"To see a child from 10 years old to making his international debut has to be a moment of great satisfaction and of great pride."
Shaw was one of 18 Southampton players on international duty this week - a proud moment for Pochettino only tempered by the negative impact it could have on Saturday's trip to Crystal Palace.
"I always enjoy watching my players when they play for their national sides," he said. "It was really great to see Luke's England debut, and Adam (Lallana) made a good contribution in the second half.
"I was very pleased with their performances on Wednesday, but it's always a difficult moment when you have a lot of players away.
"Overall, when you include the Under-21s, Under-19s and Under-17s, we had 18 players out of the club so it's good to have them back and to be able to welcome them into the squad.
"All of the players that have been away on international duty might have a little bit of fatigue, especially those who have travelled long distances like Maya Yoshida and Victor Wanyama, who have just got back.
"Of course there are some minor problems that we need to assess with certain players, especially those who have been away."
Southampton will be looking to do the double over Palace on Saturday, having comfortably defeated the Eagles 2-0 earlier in the campaign.
Pochettino is, however, aware that the south Londoners now represent a much bigger threat, with Tony Pulis having led the side from the foot of the table to as high as 14th place.
"It's clear that with their change of manager they have become a much more aggressive side," the Argentinian added.
"We've reviewed a lot of the home games that they've played recently, and they've shown they are a very aggressive, physical side. They use a lot of long balls so we're going to have to be aware of that.
"It's important that we balance out their desire to win with our own desire to win. We have to be at 120 per cent to match their aggressiveness and their need for points.
"If we're able to do that, I think we'll have a good chance of winning the game."