The Premier League Toffees will travel to Whaddon Road on January 7 after Hereford's Sam Clucas had levelled Shaun Harrad's penalty only for Kaid Mohamed to head the winner in the second half of extra-time.
"In extra-time we could see penalties looming but we were the only ones who were going to win the game in that half-an-hour," said Yates.
"We were the ones doing all the attacking and we got what we deserved in the end.
"Hereford were set for penalties and it was just a case of whether we could break them down.
"We were frustrated with the goal. We thought the referee got the corner wrong in the first place.
"Scott Brown had one save to make in the first half and it was a really good one. But apart from that, he has not had anything to do."