The Blues have not won any of Lampard’s first three competitive games in charge, having drawn in Wednesday’s Super Cup game with Liverpool and losing on spot-kicks.
Chelsea looked strong in the first half hour on Sunday and took the lead early through Mason Mount, but were pegged back by Wilfred Ndidi’s second half goal for the Foxes and narrowly held on for the point.
Lampard acknowledged he will be judged on results and admitted frustration over the performance despite the talent he believes is there.
In fact, Lampard believed the Blues' performance in their heavy defeat to United was the more pleasing one in their first two Premier League games.
“It's a results business,” the former Derby boss said after the game.
“It's strange because the performance against Manchester United overall made me happier than today even though it was a 4-0 result.
“We need both. I believe we have both in us because we have good quality, so we have performances in us as we've shown that already.
“There's moments and personality moments in the game when we need to be tougher. We have to have game management.
“If a game turns slightly, and it didn't even turn against us big time in the first half as it was just a feeling of them having more possession and being in the game, we're good enough to wrestle that back and move the ball better.
“That's something all of us can work on.”
Lampard was loath to cite fatigue after their midweek fixture as a factor in the result against Leicester, but conceded it was on his mind.
“I hate the tiredness excuse, but it has to be a factor in the second half of the game," Lampard added.
“I saw Liverpool play and I know it would have been tough for them, we were all in it, we had 120 minutes, we flew home the next day up to five in the morning, so I think it might have affected us later in the game.
“But I think that if that is a factor, we can take it out of the game by being better on the ball and too many times we allowed the counter attack.
“I feel for the players on that one, but I don't want to use it as an overriding excuse.”