Despite splashing the cash during the summer, few took seriously talk around the south coast of a push for a European finish.
Mauricio Pochettino's side, though, are doing their best to disprove the doubters and moved up to third with Saturday's impressive 2-0 win against Fulham.
Those three points made this Southampton's best-ever start to a top-flight season and forward Rodriguez believes they have yet to reach their peak.
"It was really good," he said of the performance at St Mary's on Saturday.
"We were very controlling of the game and we created so many chances and the reward is all down to how hard we've worked and to the belief which we've had from day one.
"It is no shock really. We know the performances that we're capable of and to improve upon for the next game.
"It's a great place to be at the moment, and everyone is the camp is enjoying it and loving it.
"It's great competition throughout the team from the back and up front it's all a challenge, but it's a good one and a healthy one because everyone wants each other to do well.
"It's the same throughout the team, and there's a really good atmosphere for us to be involved in."
Rodriguez played a key role in the defeat of Fulham, first flicking a James Ward-Prowse corner onto Rickie Lambert to open the scoring after 20 minutes.
The England international returned the favour late in the first half, heading across a fine ball from Adam Lallana for Rodriguez to nod home at the far post.
That proved the end of the scoring but, in truth, Fulham were fortunate to have left St Mary's on the back of just a 2-0 defeat.
Martin Jol's men were left chasing shadows from the outset and were unable to cope with Saints' pressing game as the hosts picked up a sixth clean sheet of the term.
"It's always pleasing to score a goal and to play like we did I think was unbelievable, so we're all very chuffed with it," Rodriguez said. "We pressed really high and it came off for us.
"We worked really hard by winning the ball in good places and creating a lot of chances as you can see from the stats so it was a really enjoyable game.
"It's enjoyable because the hunger is there which comes from the pressing and working hard.
"We all enjoy the pressing when we're creating chances, but the main thing for us is keeping clean sheets."