The young Foxes went 1-0 down in the first-half after Daniel Barbir poked in from close-range to give the visitors the lead going into the break.
An improved second half from the hosts saw Danny Rowe earn a penalty just after the hour mark. The No.10 stepped up and sent goalkeeper Ethan Ross the wrong way to level things up at 1-1.
Several good opportunities followed for City including efforts from Brandon Fox and Hamza Choudhury, but it was Andre Wright who struck at the other end in injury time .
Reflecting on the loss, Peake told LCFC.com: “I thought we were slow to get out of the blocks in the first-half, especially going forward. Our energy levels were low which hopefully will be highlighted on the analysis.
“We didn’t really put the work-rate in to make angles to receive it and we didn’t close them down high up the pitch as we’ve done most of the season.
“In the second half we came out with the right approach – a higher tempo – and obviously got the equaliser. To me, we looked the most likely to go on and win the game.
“It’s disappointing that we’ve conceded from two set-plays and with the ball bobbling around the six-yard box and them getting on to it first.
“In the first-half we got away with it because Max Smith-Varnham made a miraculous double-save to deny them a goal in a similar situation.”
Putting the result behind them, Peake’s youngsters now turn their attentions to the fourth round of the FA Youth Cup.
City face Chesterfield at King Power Stadium on Monday 19 January, having beaten Wigan Athletic 1-0 on the same soild in the third round.
“It’s another home tie on a Monday night so the atmosphere will be different to playing at Belvoir Drive,” Peake added.
“Most of the players aren’t really used to a 7pm kick-off unless they’ve performed for the Under-21s this season.
“It’s at King Power Stadium so it’s a good occasion for them. It’s a tie they can definitely win but we know that there are shocks within the tournament.
“We’ve already seen big Premier League youth clubs knocked out already. There’s a lovely carrot at the end of it with either a trip to Everton or Southampton should we be able to progress.
“We’ve got to get past Chesterfield first and make sure we’re fully firing because we’ve not been as prolific in front of goal in the last three or four games as we have earlier in the season.”