"I have heard people saying that we are under pressure, but we are under no pressure. That was last season, trying to stay in the top division," he said.
"It was disappointing, the way we lost to Arsenal, but we will bounce back."
Despite their last-gasp defeat at Arsenal the 27 year old feels the Foxes can be satisfied with recent results.
"We were of course disappointed to lose last week, especially the manner of the defeat, but if you had offered us six points from Liverpool, Man City and Arsenal, we would certainly have taken it," King told BBC Radio Wales.
"Things are going well and you can imagine the training ground is buzzing at the moment.
"It is brilliant to be playing for the team top of the Premier League. I am enjoying every minute of it."