The two clubs met on Saturday for a 0-0 draw.
King cannot play matches in quick succession due to a chronic knee condition but is hoping to play a key part in Spurs' run-in after coming so close to a Champions League place four years ago.
"I think we've got a stronger squad than them," King said. "You've seen the likes of David Bentley and Gareth Bale coming in and they're playing great, and they've added to the team, and that's the beauty of having the kind of squad we've got.
"We believe we can still do it, it's going to go down to the wire, but the best team at the end of the day will get fourth spot."
King himself would relish the chance of playing in the Champions League next season should Spurs get in the top four.
"For the last few years I've felt the club's always been going in the right directions, and finally we've got a manager who hopefully can do that for us," King said.
"The Champions League is something I sit down and watch and look forward to on the Tuesday and Wednesday. I probably would have liked to have played it a bit earlier in my career, but that's the way it goes.
"Any footballer, playing at club level, aspires to play in the Champions League against the best players around.
"You want to play in those games, the atmosphere, against the best players, that's what you strive to do, you go into training every day and work hard to test yourself against the best.
"All the lads here love watching the games and we'll talk about them on the Tuesday and Wednesday leading up to the games and there's a hunger for us to achieve that."