King scored in Leicester's 2-2 draw with West Brom on Tuesday as Claudio Ranieri's side looked to have dropped two points in their Premier League challenge.
But it looked a good result in light of defeats for title rivals Arsenal, Tottenham and Manchester City on Wednesday.
And Wales international King now wants the Foxes to push on, saying they cannot afford to blow all of their hard work during the title run-in.
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"We have to make sure we finish strong to actually achieve something rather than say, 'We had a good three quarters of the season and it fizzled out.
"It has been brilliant, it is hard to put your finger on it at the moment because we haven't actually achieved anything this season yet.
"But we are enjoying the ride, I speak for everyone when I say we are playing full of confidence as you have seen but 10 games to go is a long way."

The Foxes have not dropped out of the top four since October and King dismissed suggestions only qualifying for the Champions League would be a disappointment.
"No, I don't think anyone in there is thinking that. We are absolutely buzzing where we are at this stage to even be considered in that conversation and that sort of breath," he said.
"People are saying Champions League football which is brilliant, but with 10 games to go there is a lot of points to be won, so we have to make sure we are there or thereabouts."
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