The Foxes dominated for large periods of the game but it was the home side who drew first blood on the half hour mark through James Rodriguez's curling effort from outside the box to give Carlo Ancelotti's men the lead.
After a second-half onslaught, the visitors found their well-deserved equaliser via a Jordan Pickford error, after he fumbled Youri Tielemans' pot-shot effort from outside the box to gift the Belgian his sixth of the campaign.
Both sides had chances to win the game in the closing stages, but neither could find a winner and were held to a stalemate.
Leicester must adapt to Ayoze Perez
With Jamie Vardy recovering from a minor hernia operation he undertook last weekend, Ayoze Perez has so far been tasked with filling the large gap the Foxes talisman occupies when fit.
For the large part of his two-game stint as the lone striker, the Spaniard has performed well, but as expected, he has his own style of forward play.
Whilst Vardy prefers to sit on the shoulder of the last man, Perez instead seems more comfortable dropping deep to win the ball which would leave the rest of the squad with no real focal point up top to work with.
The likes of James Maddison and Tielemans thrive on Vardy's jinking runs into the channels and at times in Merseyside on Wednesday, they and others would try the same for the former Newcastle United man with the end result often not going their way.
It may only be for a short period, but if and when he plays that role again for Leicester, they may have to look at tweaking their style ever so slightly to accommodate for the way Perez plays.
Does Cengiz Under deserve to start?
Having so far seen him in flashes, there is no denying that Cengiz Under has an abundance of talent. His goal at Brentford in the FA Cup and second-half substitute display on Wednesday will have filled both Leicester fans and his manager with confidence that he can suit the style of English football.
The 23-year-old replaced Marc Albrighton as the Foxes went in search of an equaliser and whilst he didn't get on the scoresheet, his ability to go past players with ease and take a shot on goal was key in helping to break down what had been a very strong defensive display from the Toffees.
The man he replaced, Albrighton, has been an influential player in recent times however with no Vardy to cross to in the box, Albrighton's main weapon isn't as effective as it would normally be.
It isn't completely out the question that Rodgers could assess that and bring Under in from the start against Leeds United on Sunday and look to give the Turkey international the chance to stake a claim for a regular starting spot in the coming weeks.
Ndidi injury concerns yet again
Despite another strong performance on the road for Leicester again, there will be worry over the state of Wilfred Ndidi's latest injury.
The Nigerian had to be substituted in the first-half after complaining of a tight hamstring, with Foxes boss Rodgers stating that they will have to look into the problem before they can confirm how long he is out for.
Whilst the East Midlanders have a capable back-up in Nampalys Mendy, Ndidi is one of the most important cogs in the side and with injuries plaguing him over the last year, the last thing anyone associated with Leicester wanted to see was the 24-year-old limp off.
It was around this stage last season that Ndidi suffered an injury, coinciding with a difficult patch of form for the Foxes and they will be hoping that history isn't repeating itself once more.