Mauricio Pochettino's side moved third on Saturday after a 4-1 win over Hull City as Southampton made it eight Premier League games unbeaten.
However, Rodriguez is keen to ensure Southampton do not lose their momentum, stating that the team can still go higher in the table.
"We put effort and hard work into (the win over Hull). It showed in the result there that we deserved it," he said.
"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 was called up to the England squad for the first time last week by manager Roy Hodgson for the friendlies against Chile and Germany on Friday and Tuesday respectively.
Team-mates Adam Lallana and Rickie Lambert were also selected for the fixtures, with Rodriguez eager to take what he can from his experience with the national side.
"I am not sure what to expect," the striker continued.
"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."
