The Dutch international produced two fantastic saves to keep the Foxes at bay in the first half but was then at fault as Jeff Schlupp volleyed home the winner in added time.
Michel did brilliantly to deny Schlupp and Andrej Kramaric before Andros Townsend converted from the penalty spot to put us 1-0 up.
It was then the turn of Mark Schwarzer to thwart Roberto Soldado and Erik Lamela as we looked for a second but the visitors levelled through Leonardo Ulloa with seven minutes remaining.
Two minutes into added time, Danny Simpson crossed from the right, Schlupp turned a volley on target and the ball squeezed past Michel and home.
“I made two good saves but it wasn’t enough and I made the mistake at the end with the second goal,” reflected Michel.
“If it happened earlier in the game maybe I could have turned it around but it didn’t, it happened at the end and that makes it even worse.
“Things go so quickly and when the ball goes in, you feel horrible. Even though there were only a few minutes to go, you just hope you can get the ball and get something back.
“It just keeps going around in your head and as I said, if it happened in the first minute it’s different. In a way it made it worse because I made some good saves in the first half.
“That’s football. It's all part of the job. You can’t be gutted for too long. I am now, obviously, but you have to move on.”
Looking at the game as a whole, Michel agreed with Mauricio Pochettino’s view that we needed a second goal to kill the game off.
“We said at half-time that we had to continue in the same spirit and we created some more chances but against every team you play in England, you have to be switched on until the last seconds,” he added.
“Leicester continued to believe and got the win. But I think we have to blame ourselves, we had the chances, we were 1-0 up and at home, so there is only one team to blame and that’s us.
“Wednesday is a big game ahead and we have to focus on that now.”
We travel to Sheffield United for the second leg of our Capital One Cup semi-final on Wednesday. We lead 1-0 from the first leg with the winners through to the final at Wembley.