Marco Asensio struck twice to help send Villa into the quarterfinals.
Martinez told the VillaTV Post-Match Live show, “It was dangerous. It was a tricky game. We were the favourites to win against a Championship side fighting relegation.
“They sat in a low block, and we struggled against low blocks lately. They had a few counter attacks, actually five minutes before we scored, they had a clear chance to score.
“We experienced that before. We played Forest, low block, Ipswich, low block, and we struggled to win in the Premier League.
“I think we did a good job today. We should have won by four, five goals.”
Martinez admits he's keen on a long Cup run.
He added: “It’s massive. I won it three times with Arsenal. I know the feeling. I know that trip to Wembley.
“For me, when I won it with Arsenal last time, it was one of my best days since I came to the UK, so I’m trying to tell all the young lads like Morgan, like JJ, how important it is to win this cup, and for the supporters to go to Wembley.
“My first target with the goalie coach is to take Villa to Wembley, and I won’t stop until I do it.”