Thrashed 4-0 at Manchester United last weekend and beaten on penalties by Liverpool in the European Super Cup on Wednesday, Lampard's side took an early lead through Mason Mount's first goal for Chelsea.
But Wilfred Ndidi atoned for the costly mistake that led to Mount's opener as the Nigeria midfielder headed Leicester's well deserved second half equaliser at Stamford Bridge on Sunday.
Chelsea's vibrant start was replaced by a woeful collapse that could easily have led to a Leicester winner.
Lampard insisted tiredness was part of the problem as Chelsea wilted following their draining penalty shoot-out defeat against Liverpool in the European Super Cup on Wednesday.
While the long trip back from Istanbul took its toll on Chelsea in the second half, Lampard wasn't happy with the way his team failed to capitalise on their early dominance or with their failure to manage the game better.
"The first 25 minutes was how we want to play and the rest of it wasn't. We left far too many spaces. That was a disappointing thing for me that we couldn't sustain the early part of the game," Lampard said.
"I don't expect that 100 miles an hour start to be maintained all the time but we have to keep the ball better when we rest.
"We have to have more personality, we saw that in midweek, but today we didn't have that.
"I hate the tiredness excuse but it has to be a factor in the second half. I feel for the players on that.
"If that is a factor we can take that out of it by being better on the ball so we don't have to run as much.
"There's game management. We have to be tougher. There are some real lessons from today."
Baptism of fire
Lampard will look to finally get his first win when Chelsea travel to Norwich next weekend.
But with just one year of managerial experience at second-tier Derby last season, Lampard knows he is facing a baptism of fire with Chelsea.
The Blues legend is unable to sign players due to a transfer ban, while star playmaker Eden Hazard was sold to Real Madrid in the close-season.
"We have had a tough start, to go to Manchester and get beaten the way we did then lose the Super Cup when I thought we were the better team," Lampard said.
"It's a results business clearly. The performance against Man Utd, and certainly the Liverpool game, made we happier than this one strangely.
"In the circumstances there are some difficult elements to this year. As a new manager I couldn't bring players in and we lost Eden, who was such a huge player at this club."
Lampard had been given a thunderous reception in his first game as Chelsea manager at Stamford Bridge.
His adoring fans weren't so happy at the final whistle, but Lampard said he was touched by the welcome home.
"It felt great. It was a big special moment for me, to manage the club at Stamford Bridge is the stuff of dreams," he said.
"It's my club, I played here so long and I'm slightly disappointed we didn't get the win but I'm thankful to the fans.
"If there was any frustration from the fans, it was shared by everyone on the bench. We are all in it together."