The England international was delighted to get the job done following three Premier League losses since Christmas.
“The cups are really special to us and the fans. I've experienced great runs here and it's something you never forget, so hopefully we can do that," said Rodriguez, who struck after just eight minutes to set Sean Dyche's men on the way to victory.
“It's always nice to score. I feel as though I'm getting in good positions, but it was important to get the win today," he added.
“We wanted to show our intent and get as many goals as we could to kill the game off.
“Credit to them. They came back with a couple, but I thought we showed our resilience and played smart and it was a good game.
“The performance we put out there was really good for the lads and hopefully we can kick on."