The Argentine coach was appointed in controversial circumstances after the unpopular dismissal of Nigel Adkins but oversaw the Saints' 3-1 defeat of Liverpool on Saturday
Rodriguez bagged the third Saints goal in front of a record Premier League attendance at St Mary's after Morgan Schneiderlin and Rickie Lambert had opening the scoring.
And the £7 million signing from Burnley is enjoying the added freedom afforded to him by Pochettino since the controversial sacking of previous boss Nigel Adkins.
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"He's said that to everyone and you can see by the way we've played that he's had a massive effect on us. Everyone knows how to play - we're pressing high and don't give anyone respect.
"The belief we've got is fantastic and we've just got to carry it on. We feel we shouldn't be where we are. We're more than good enough to beat any team and want to be higher."
Southampton now lie four points clear of the bottom three on 31 points and Rodriguez hopes another two wins will be enough to keep them up.
"We'd like to think that [two wins will ensure survival], but we're just going to concentrate on the next game," he added.
"We'll have a look at Chelsea and work out how to go against them and hopefully do what we did today.
"Chelsea have great players and are a great team but we've got to concentrate on ourselves and believe we're more than good enough to go out and get another result."
The 23-year-old drove forward from the centre circle before beating goalkeeper Brad Jones at the second attempt to wrap up the scoring on the south coast.
"I decided to drive forward and got a little bit more space than I thought I would," Rodriguez recalled. "Then I got a little bit of luck from the palm down – and I'm chuffed to bits!
"We stuck to the game plan and it's another massive win, one we felt we deserved which is the best thing about it, against a great Liverpool side that has great players."