The Southampton trio were called up by England boss Roy Hodgson for the friendlies against Chile and Germany later this month.
Rodriguez has been rewarded by Hodgson after scoring three goals in 10 matches during Southampton's superb start to the season and Pochettino has praised his inclusion.
"Jay fully deserves his England call-up," said the Saints boss. "He's been on a really good run lately.
"We're really proud of our three players in the England squad. Can they go to the World Cup? Why not?
"Not only those three, but the squad has improved in the nine months that we've been here."
"The players are the protagonists here - they deserve all of the credit, not me. We have a great structure here."
Pochettino confirmed that Dani Osvaldo will have a fitness test on Friday to determine whether he will be available for Saturday's visit of Hull City to St Mary's, while Guly do Prado is expected to be out for two months after undergoing a knee operation on Wednesday.
Southampton have received plenty of plaudits for their start to the season but Pochettino has warned against complacency creeping into his squad.
"Compliments can be taken negatively or positively," he said. "We're in the headlines and we appreciate that, but it changes nothing."
"From 10am on Friday until 5pm on Saturday, we're completely focused on facing Hull. There will be nothing else in our minds.
"Right now, we have to think as a team. After that, our players can think about their national teams."