The 24-year-old was last month given a surprise call-up along with club-mate Adam Lallana for the international friendly double-header at Wembley.
The uncapped pair both started in England's 2-0 defeat at the hands of Chile, with Lallana impressing enough to also begin the disappointing 1-0 home loss to Germany days later.
That was a match Rodriguez was forced to watch from the sidelines, with Hodgson not giving him any more minutes after a debut that led to criticism from some quarters.
However, such talk has had little impact on the former Burnley man, who appears to have cocooned himself away and focused on life with Southampton.
"I don't really listen to whether anyone says anything," Rodriguez said. "Obviously I wasn't happy with my performance in the game, but the experience was unbelievable for me.
"I took a lot of positives from that, but I would have obviously liked it to have gone better and to get the win. It was a hard game and I thought Chile played really well."
Lallana's displays have seen him widely tipped to be included in Hodgson's World Cup squad, but the same cannot be said for Rodriguez.
Some bookmakers price him at 10/1 to be on the plane to Brazil - the same odds as West Brom's uncapped Saido Berahino - but that will not stop the Southampton man trying.
"I think you've always got to set your targets as high as you can and I think that is the highest target you can try to achieve," Rodriguez said of a potential World Cup spot.
"It would be a great feeling to go to a World Cup, but I have a lot of hard work to do. I need to keep trying to improve as a player for Southampton."
Rodriguez has certainly reacted in the right way since returning to club matters, playing a starring role in Saturday's 1-1 draw with Manchester City.
It was a match that ended Saints' three-match losing streak - the first under manager Mauricio Pochettino - and a result that will give them renewed hope heading to in-form Newcastle this weekend.
"The City game has given us a buzz, but we have always had confidence and belief even when we were getting beaten," Rodriguez said.
"I thought the performances were still good and I think it shows to keep belief in the team because we can get results against a great side.
"I think the manager was really happy with the way we were playing. When times are hard, you've got to believe more in what we are doing and I think we have done.
"Newcastle are doing really well. They are higher than us in the table and that reflects how well they are doing.
"We know they are a strong side, it is a good atmosphere up at their place as well, so it is something to look forward to and I hope we can stop them from keeping their run going."
If Southampton are to get a positive result in the north east, much could depend on top scorer Rodriguez.
The forward took time to settle after what was at the time a club record B£6million move from Burnley last summer, but he has thrived since Pochettino replaced Nigel Adkins at the helm in January.
"Since he has come in he has given me the belief, the confidence, and shown me the way to play," Rodriguez said.
"It has obviously helped me massively. It is all credit to Mauricio for helping me improve as a player.
"It is a good team to be involved in. We keep the ball, play well and we work hard. We're all honest lads and it is a good team."
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