The Argentinian took to the St Mary's helm in controversial circumstances in January but has quickly won around supporters with an exciting brand of pressing football.
That was evident in the high-profile scalps of Manchester City, Liverpool and most recently Chelsea, who on Saturday left St Mary's on the wrong end of a 2-1 scoreline.
Rodriguez opened the scoring against the reigning European champions, capping what was yet another fine performance from the former Burnley attacker.
The 23-year-old had initially struggled for form after his £6million summer arrival but has flourished since Pochettino's arrival on the south coast.
"The manager has put his faith in me," Rodriguez said.
"He gives you belief that you should be on the pitch because he's played me and given me a chance.
"All I can keep doing is to try and do my best for him, and for the team.
"I was chuffed with the goal but, like I always say, it's the three points that matter."
It was fine all-round performance from Southampton, who went ahead in the 23rd minute when Rodriguez finished a superb team move by slotting past Petr Cech.
John Terry was allowed to level unmarked from a corner 10 minutes later, only for Saints to hit back immediately through an exquisite - and ultimately decisive - 25-yard Rickie Lambert free-kick.
"It was a good performance," Rodriguez said. "We worked really hard and I thought we deserved the win.
"Obviously it was a great goal from Rickie, which was key, so it was a good three points.
"We just have to carry on that form we've got. We did well against Liverpool and worked hard during the international break.
"We know how good Chelsea are and I thought we played really well."
Southampton now sit 12th in the standings - their highest position since returning to the Premier League - although only four points separates them and the bottom three.
"It's still tight down there, so we're going to concentrate on ourselves because that's all we can affect," Rodriguez said.
"Our next game is our most important game - that's what we all think and we'll be working all week for that.
"It's important that we get three points to move us up the table.
"We'll work out a strategy and a tactic to play against them, and work hard to win the game."
That match is away at Reading - a mouth-watering duel between Pochettino and the man he controversially replaced at Southampton two months ago, Nigel Adkins.
"It will be a great occasion against Reading but we're just going to concentrate on ourselves and getting the three points," Rodriguez added.
"We'll work hard all week and focus on Reading and hopefully moving up the table."