Xherdan Shaqiri's fine first-half strike looked to have lifted the Potters out of the relegation zone, with Stoke on track for a first away league win since October.
But with Stoke seemingly comfortable in the game, Butland misjudged a Marc Albrighton cross and deflected the ball into his own goal.
The goalkeeper would later make two saves from Riyad Mahrez, with Harry Maguire and Matty James both hitting the woodwork in the closing stages, and Lambert defended the player.
"He's the best goalkeeper in Britain, he's absolutely fabulous," Lambert told Sky Sports.
"You put yourself up, dust yourself down and go again. Great players make mistakes, it's how you come back. Butland's been great since I came in. It's not the first or last mistake he will make."
Stoke have taken six points from their last five games under the Scot and Lambert hailed the improvement his side have shown, picking out Shaqiri for praise after he scored for the third straight Premier League game.
"We were outstanding, played ever so well, defended really strongly as a team and we looked great," Lambert said. "A threat on the counter, the performance was outstanding and maybe should have won the game.
"Shaqiri had a good chance to win it. I think he's a real world class footballer, he makes things happen. Unlucky with his vision in second half and he makes things happen, he's playing ever so well and I couldn't fault them.
"We're well in games and that's a big improvement, I've only been here a few weeks but the turnaround has been vast and we're playing well enough to win football matches."
Although Leicester ended the game well on top, Foxes coach Claude Puel felt a draw was the correct result.
"Not enough to win today," Puel said. "We could have, but we could also have lost so perhaps a draw is fair.
"Their goalkeeper made some good saves, but we also conceded chances.
"I thought we started well, with intensity, but it became too slow to find space. It was better second half, but without a clinical edge or a little luck to find a winning goal.
"We needed greater desire to score, to attack the box together. We did it at times, but not consistently enough. When we did, their goalkeeper made some fantastic saves."