The 24-year-old, along with Saints colleagues Adam Lallana and Rickie Lambert, was included in Roy Hodgson's squad for the November friendlies against Chile and Germany, winning his first cap against the South Americans at Wembley.
Since his Three Lions appearance, Rodriguez has scored five goals in his last six Premier League outings, including a brace in the 3-0 Boxing Day win over Cardiff.
And the former Burnley forward hopes his club performances can keep him on Hodgson's radar.
"Obviously it is an honour to play your country and a confidence boost when you do get selected," he said.
"It was a nice taste and you obviously want more of it so hopefully I just can just carry on improving and maybe you never know.
"All you can do is keep your head down at your club. You work as hard as you can to try and improve as a player and hopefully then it pays off.
"I have said to myself I want to improve on last year and hopefully I can carry on improving. I want to score as many as I can in each game, so hopefully I can."
And Rodriguez admits the freedom he, Lambert and Lallana are given is bringing out the best in the trio.
"It is nice, the way we play suits me at times, we can try and get in behind the defence and hopefully be around the box to put the goals in so it is nice at the moment," he said.
Southampton's win at Cardiff was their first in seven games, and Rodriguez hopes the three points and the return of several players from injury can spark an improved run.
"We felt we needed that result," he said.
"We have kept the belief in what we want to do and the confidence and team spirit has always been there so it's nice to get the three points that we deserved.
"Of course you have injuries in the camp, that's always disruptive.
"But I think the lads that have come in have done extremely well. We have got a great squad that has shown by the results and hopefully we can continue to pick up points."
The Saints head to Everton with the Toffees having lost for the first time at home this calendar year against Sunderland on Boxing Day.
"Maybe it is a bad result for us or it isn't," said Rodriguez.
"But we know Everton are a great side and are doing extremely well so it will be a tough game, but we like to keep the way we play and hopefully take it to them and get the three points up there."