Leicester have forced a third-round replay with a 2-2 draw against Manchester City at the Walkers Stadium on Sunday.
Debutant Sol Bamba gave the Foxes a sensational first-minute lead in the east Midlands but goals from James Milner and Carlos Tevez had appeared set to send the visitors through.
But City keeper Joe Hart fumbled Paul Gallagher's cross to allow King to tap home an equaliser.
The hosts created several opportunities to win it, with defender Jack Hobbs heading over the bar with the best of them, but King does not believe failing to win at home means the Championship side have wasted their best chance of progressing to the fourth round.
King told ESPN: "You have to look at the players they brought in to their side and the quality in their squad and to get something was probably what we deserved.
"We were the home side and we are confident and we don't fear anyone and it showed.
"They are strong at home but we have given ourselves a chance and we are in the hat for the next round. Having played how we did we could have come away with that win."
King also paid tribute to the performance of Bamba, with the former Hibernian defender proving a constant menace at set-pieces.
"Our scouting staff have obviously done their homework and he was exceptional today, it looked like he was going to score from every corner."