Penalties from Taylor and Jack Collison gave the Hammers a 2-0 victory at Turf Moor in the fourth round of the competition.
Despite failing to score in open play, Taylor believes that there is little argument against West Ham taking their place in round five.
"We didn't have a particularly great first half, but the manager came in and changed the formation and personnel at half time, and we went out in the second half and put them on the back foot," he told the club's official website.
"I know we've won it with two penalties but I still thought that we were the better team and that it was a fully deserved win."
West Ham continue their Premier League campaign on Saturday when they welcome Aston Villa to Upton Park.