Spurs came into Tuesday's meeting at Stade Louis II needing at least a draw to keep their hopes of progressing from Group E alive, but they were distinctly second best as the hosts ran out 2-1 winners.
Kane's penalty levelled the scores four minutes after Djibril Sidibe's opener early in the second period, but Spurs found themselves behind again just over 30 seconds later as Thomas Lemar fired home.
Monaco sealed their qualification as group winners with victory, but Spurs have only third place and the Europa League to play for, leaving Kane to rue Monaco's winner so soon after his equaliser, as well as Spurs' two home defeats earlier in the campaign.
"We're disappointed obviously, I don't think we were good enough today anyway but we got ourselves back in it at 1-1 and it was schoolboy to concede straight away after that," Kane told BT Sport.
"We've got to try and push and get another but we conceded straight away and that took the stuffing out of us and we didn't have enough to come back into the game.
"Obviously we're gutted. We wanted to go far, we're all disappointed but it's something we'll have to deal with, dust ourselves down and get ready for the weekend [against Chelsea].
"Losing two of our home games... in this competition it's got to be a fortress. Although we're at Wembley it's no excuse, we've got to make it difficult and use it to our advantage and we didn't.
"It's always difficult away from home in the Champions League, the home games is where we should have been better."
Spurs wasted a gilt-edged opportunity in the sixth minute when Son Heung-min went through one-on-one but was denied by Danijel Subasic, but Kane said the South Korean could not be blamed for a listless defeat.
"It was a big chance, Sonny knows that, nine times out of 10 he'd put that away but we can't use that as an excuse, we just weren't good enough," he said.