Harry Redknapp's side have shipped eight goals in their least two Premier League games -- defeats to Arsenal and Manchester United that have dented Spurs' bid to finish in the top three.
The Spurs manager claimed individual errors were responsible for all three of United's goals in Sunday's defeat, and centre-back King agrees that performances have not been up to scratch.
A repeat of those mistakes against League One Stevenage at White Hart Lane could spell embarrassment for Redknapp's team and deny the club the chance to face top-flight strugglers Bolton Wanderers in the sixth round.
King made it clear there must be an immediate improvement if Tottenham are to maintain the progress they have made so far this season.
The defender said: "You're not going to beat teams like United if you're not concentrating and it was a bit of a lesson.
"You can't fault the work rate and we gave a good account of ourselves for the majority of the game but if you fall asleep at vital moments, you get punished.
"To allow them a free header in the six-yard box on the brink of half-time was disappointing. It shouldn't be happening.
"We lifted ourselves but we went to sleep on a throw-in for the second goal."
Stevenage drew praise for their efforts in holding Spurs to a scoreless draw in the first leg.
With a weekend trip to follow the midweek cup clash, King knows there will be no easy games between now and the end of the season.
He added: "There are tough games all the time because there are teams in the league now that are fighting for the league, fighting for European qualification and fighting against relegation.
"It will be a dogfight until the end. Every team wants to pick up points and we're the same. We want to try to finish the season on a positive note.
"We've got a chance to get through to the next round of the FA Cup this week.
"We have to pick ourselves up during this week, be ready for that and keep going."
Tottenham's recent dip in form has not gone unnoticed by Stevenage, who currently sit in seventh spot in League One, one place outside the play-off zone.
Skipper Mark Hudson said: "We have got to capitalise on that. It has not been a great series of results for them and we have to back ourselves.
"We have to think we can go there and win the game because if we don't we will come unstuck.
"There is plenty of belief in this dressing room. It's a big game for everyone and especially for me as I'll be leading the team out at White Hart Lane."
He added: "It might seem strange but there was an air of disappointment in the dressing room after the first game.
"Everyone was saying 'well done' and patting us on the back but that felt strange because we had only drawn the game. There were mixed emotions to be honest."
Striker Craig Reid warned Spurs will be making a big mistake if they underestimate their opponents, despite playing on home soil.
Reid said: "If that's what they want to do then let them do it. We've beaten some big teams like Reading and Newcastle, and drawing with (Spurs) the first time just shows we can mix it with them and Wednesday will be another big test for us.
"It's a great achievement by the club. We've been used to a lot of success, especially against bigger clubs, and hopefully Wednesday will just be another stepping stone and another story to tell."
Source: AFP
Source: AFP