The striker burst clear and slotted home in the first-half, after winning a 50-50 challenge with the home side’s keeper, Julian Speroni.
Rodriguez’s goal came just a few days after being involved with England in the last friendly before Roy Hodgson names his squad for Brazil.
Although the 24-year-old did not make it onto the pitch in the 1-0 win over Denmark, he could yet earn a place at the World Cup. Rodriguez would love the opportunity, but says he will not be expecting anything.
“Hopefully it happens again and hopefully I can carry on scoring as many goals as I can when the chances come my way,” he said.
“It’s always a brilliant feeling to be selected for your national side, you learn so much when you go away and it’s a great feeling to be a part of that.
“It was great to see Luke (Shaw) and Adam (Lallana) in there, because they’ve been fantastic all season and, for myself, it was just nice to see them play.
“It was a good all-round performance and a good one to be involved in.
“It’s a good thing to be included in the 30-man squad, because it was an unbelievable feeling for me.
“But I won’t expect anything at all, I just want to keep on improving by working hard and that’s all I can concentrate on and focus on, because that’s all I can effect.”
Saturday’s victory ended a run of three defeats for Saints, and Rodriguez was thrilled that the team have put that spell behind them.
“It was important for us to get back to winning ways,” he said. “The game was tough for us, but I thought we defended really well and played really well as a team, and deserved it.
“It was a tough game and Palace played really well, but we stuck together and defended well and controlled the game at times so it was a good performance.”