"They'd knocked City out when I wasn't at the Club in the quarter final a couple of years back and it means a lot to us and the fans to proceed in the competition," Hart told City's website.
"Everyone's happy, we've won the game and we just want to do well in the cup and keep winning.
"This is a huge competition and the boss regards it as one of the biggest that clubs can be involved in. We just want to keep doing well in it and keep everyone happy."
Following a tricky first game at Upton Park, last night's third round replay proved to be a tense affair before Elano struck in the 73rd minute.
"It was a bit of a graft when we played them at Upton Park because it was on the back of the Christmas period and the boys were tired," Hart added.
"So to grind out a result down there and then come here and do the business is good."