Spurs have only won two of their last nine league games, a run of form which has seen North London rivals Arsenal overtake them in the Premier League.
However, King has said that the squad must pull themselves together as there is still plenty to play for.
"I think the earlier we have a speak together about it, the better it will be," said the 31-year-old. "The only thing that needs to be said is that we need to stick together at this time, keep going until the end of the season and keep working hard for each other. There is not a crisis in any way.
"It's up to the senior lads to lift the spirits of the rest of the lads and keep them there. It has been a long season and there are some tired legs but we have to keep pushing. We have top players.
"We have lost to Norwich but we have another big game that we have to get up for."
Spurs face Chelsea in the semi-final of the FA Cup at Wembley on Sunday.