It took just 38 seconds to take the lead through Luke Varney with Mark Rivers doubling the score before the midway stage of the first half.
But Leicester clawed their way back into the match with one from Danny Tiatto in first-half injury time and a 50th minute penalty from Johannes Gudjonsson to leave Gradi ruing the loss of two points.
"We got off to a great start and could have scored four by the time we got our second," he said.
"We were running them ragged and they had to change it, which they did.
"We scored too early in many ways. All the back four were panicking and they all looked very jittery."
Leicester boss Craig Levein also felt his side could have won but was relieved to at least pick up a point.
He said: "The game must have been unbelievable entertainment to watch because both teams were creating chances and looking like they wanted to get three points.
"It wasn't a draw that was in anyway boring or lacked entertainment. It was a smashing match.
"It just think from our point of view I am disappointed that we found ourselves in a situation where we had to claw back a two-goal deficit.
"There are loads of positives to take from the match. The biggest negative is that we lost two goals."
Crewe started off in thrilling fashion and they caught the visitors napping in the first minute.
Darren Moss broke down the right before sweeping a low ball into the six-yard box where Leicester failed to clear the danger and Varney was on hand to fire home on the turn.
It sparked an end-to-end first half in which both sides looked like scoring each time they ventured forward.
Despite Paul Henderson and Elvis Hammond looking lively, it was Crewe who doubled their lead through Rivers after being put through by Michael Higdon.
Leicester's pressure paid off though in first-half stoppage time when Tiatto finally managed to beat Ben Williams, firing home from 20 yards after Gareth Williams' short free-kick.
Five minutes after the break Gudjonsson, after being upended by David Vaughan in the area, coolly converted the penalty himself.
Both sides could have then gone onto to win it with Rivers heading against the bar and Hammond hitting the post from the edge of the area.