Saints had 18 players away on international duty in midweek, including four with Roy Hodgson's England squad for the 1-0 friendly victory against Denmark.
The match saw teenager Luke Shaw make an impressive international debut, while Saints captain Adam Lallana further boosted his chances of going to Brazil with a fine display off the bench, capped by the cross from which Daniel Sturridge scored.
Rickie Lambert and Rodriguez, the other Southampton players involved, were reduced to a watching brief at Wembley, returning to action as Saints won 1-0 at Selhurst Park on Saturday.
The latter netted the decisive goal in what was for large parts a frustrating match, latching onto a weak header by former Saints winger Jason Puncheon and then beating Julian Speroni in a 50-50 challenge to finish into an open goal.
"I thought the goal showed exactly what Jay Rodriguez is made of," Pochettino said of the 37th-minute strike.
"It showed his quality, showed his speed, showed how brave he is, showed his technique. It also shows the fact that he fully deserved the England call-up as well."
Asked if Rodriguez had the talent to play at the World Cup, the former Argentina international said: "I think he has the talent, I think he has the skill to go with the English national side and play for the English national side.
"I think the call-up to the English national side by Roy Hodgson of Jay Rodriguez was deserved, and to actually win your place you need to deserve you place to be going to the tournament.
"To be scoring goals as he did here, he is definitely increasing his chances."
The 1-0 triumph ended a run of three successive losses in all competitions for Southampton, and Pochettino believes highlighted the club's exciting future.
"I am well pleased with that win," said the 42-year-old, for whom the only negative was an ankle injury to Jack Cork, which is expected to rule the midfielder out for six weeks.
"We're well balanced, doing well, building a project and we want to continue in this way.
"I think we are showing the potential we have for the future at Southampton Football Club and we are very well pleased with the victory."
Palace managed just one shot on target at Selhurst Park, leaving manager Tony Pulis frustrated by his side's toothless display.
"I don't think it was an off-day - I thought we did all right," the Eagles boss said. "I thought we competed very well.
"The disappointing thing was that we never created more chances and more opportunities. That was disappointing.
"But they are a good side, they've got some good players and we've watched them the last three games they've played.
"They played exceptionally at West Ham and got beat 3-1 so they've got some real quality. It was always going to be a tough game and those tough, tight games we need a break and we didn't get one."
One of those breaks looked like it may come when Dejan Lovren brought down Yannick Bolasie when he was through on goal early in the second half.
The Palace fans called for the Croatia international to be sent off, but referee Howard Webb did not deem him the last man so only produced a yellow card.
"I will leave you to decide that," Pulis said when asked for his thoughts on the decision.
"We've just watched the video and the disappointing thing was the first two offsides as both Glenn Murray and Joe Ledley are onside. The linesman has given two offsides and both of them were on, through and past the back four onto goal.
"That was very disappointing and they were in the first quarter of an hour."