Saturday's 4-1 thrashing of Hull made this Saints' best ever start to a top-flight season, even trumping the 1983/84 campaign in which they went on to finish runners-up.
Rodriguez has played a key role in that success and believes Mauricio Pochettino's side can stay up with the Premier League frontrunners.
"We put effort and hard work into it," the forward said. "It showed in the result there that we deserved it.
"We went to third and we still believe we can be higher. There are no limits for us, really. We've just got to keep impressing and working hard."
Rodriguez is certainly impressing, earning a first call-up to the England senior side for the upcoming friendlies with Chile and Germany.
Saints team-mates Rickie Lambert and Adam Lallana have also been included in Roy Hodgson's squad, with the trio travelling up to St George's Park on Tuesday.
"I am not sure what to expect," Rodriguez said. "I spoke to Rickie and he just said it was a great experience and that the lads are great.
"He came back from it with a lot of confidence and it is just an unbelievable experience. I can't wait.
"You look at the players. It is an unbelievable experience playing against them, so actually playing with them will be excellent for me."
Considering Saints were plying their trade in League One three years ago, the number of international players at their disposal is quite remarkable.
Even more surprising, however, is that Morgan Schneiderlin is not one of them.
The 24-year-old was last season crowned fans' and players' player of the year and has continued to impress this term, although the the French national team has yet to call-up the former Under-21s international.
"It does surprise me because he's a player that does have the same quality as the players that have been called up," Saints manager Mauricio Pochettino said of Schneiderlin, one of Southampton's longest-serving players.
"He is a player that has amazing quality and I am 100 per cent sure it will happen.
"He needs to keep on working with the same humility, the same work ethic and it's a matter of time until he will get that call up.
"The only thing I would say to the French Federation is they should be careful because he might be able to play for England."
Source: PA
Source: PA