Mikel Merino's second-half goal in Dallas sends the reigning European champions into a last-eight clash with Belgium in Los Angeles on Friday. Spain also maintain their outstanding defensive record, having yet to concede a goal in five matches at the tournament.
Rodri, who was named Player of the Match, is pleased with the result but insists Spain have another level to reach as the knockout stage continues.
"There's a lot of room for improvement," Rodri said.
"Now we have to rest and keep improving. We're very similar teams, we want the ball, and we want to have personality."
The Manchester City midfielder believes Spain must move the ball quicker in the final third to make the most of their attacking opportunities.
"It's about small details," he said. "The first chance we had in the whole game came when we got inside. It's something to learn from for the next games. We have to be sharper because we can do a lot of damage.
"In football nowadays, in the last third you have to speed things up.
"When we broke their lines, we were maybe taking an extra touch. You have to turn quickly and find the players in attack. That's how the goal came."
Rodri also credits Spain's defensive strength to the work of the entire team rather than just the back line.
"We were able to read the flow of the game at all times," he said. "We wore them down, and we found our opening."
The Spain captain is also quick to praise his midfield teammates for their efforts on and off the ball.
"I think they played a very complete game in midfield, and I think we did too," Rodri added.
"Pedri has been the same as always, sensational, helping me clear everything he could. Even though he might not be that kind of player, he's been pressing hard to win the ball back. He's been outstanding, and the guys who came on, Mikel and Fabian Ruiz, were impressive."