The loss was compounded by injuries to midfielder Morgan Schneiderlin and goalkeeper Artur Boruc, who faces a six-week absence with a broken left hand.
Rodriguez told Saints Player: "The defeats will improve us as a team. We've got the belief in our team and the team spirit to bounce back. It's a massive week."
Rodriguez was pleased with his early goal, but frustrated Saints could not build on the advantage.
"I thought the keeper (Cech) was going to come out but he took a step back," the forward added.
"I just thought to put it in and luckily it went in the net. I was obviously really chuffed but we're disappointed with the result.
"We wanted to keep the lead and improve on it. We had chances to go on and create another goalscoring opportunity, just the last pass was off.
"It's something to look at and to try and improve on for the next game on Wednesday."
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