The result means Spurs cannot progress from Group E and need a point against CSKA Moscow at Wembley next month to finish third and qualify for the Europa League.
Lloris denied former Manchester United and Chelsea striker Radamel Falcao’s spot-kick in the first half and made a number of superb saves but second-half goals from Djibril Sidibe and Thomas Lemar gave Monaco a deserved victory.
Harry Kane offered Tottenham temporary hope when he equalised from the penalty spot but the visitors simply never found the spark required to resurrect their faltering fortunes in Europe.
“It is disappointing,” Kane said. “We got ourselves back in the game at 1-1 and it was schoolboy to concede straight after that.
“We had to try to grind out a win because we were not great tonight — the second goal took the stuffing out of us. I just don’t think we were good enough. I’m gutted — we wanted to go far but it is something we have to deal with.
“Losing two of our home games in this competition — yes, we played at Wembley this year but it has to be a fortress at home.
“We will look back and say it was the home games were we should’ve been better.”
Monaco, meanwhile, are now guaranteed to go through as group winners with Leverkusen, who had earlier drawn 1-1 with CSKA.
Pochettino took a gamble by leaving out Jan Vertonghen and replacing him with the largely out-of-favour Kevin Wimmer.
Dele Alli, however, was passed fit and there was also a first Champions League start for 20-year-old academy graduate Harry Winks.
Son Heung-min could have given Tottenham the perfect start when he was played through one-on-one by Alli but as he tried to go around goalkeeper Danijel Subasic, the South Korean took a heavy touch and the chance was gone.
That was as good as it got in the first half for the visitors, who should have fallen when Victor Wanyama and Eric Dier both took wild swings at the advancing Fabinho, with Dier connecting to concede a penalty. Falcao was unable to capitalise as Lloris guessed correctly to save his effort.
Lloris was called into action again to save Benjamin Mendy’s fizzing finish and then a feeble follow-up from Valere Germain, who was then guilty of failing to take advantage of a free header at the back post, instead heading straight into the midriff of Wimmer.
Germain was a constant menace in the channel between Wimmer and Rose, and he fired another shot wide of Lloris’ far post before Spurs traipsed off at half-time, relieved still to be level.
Whatever Pochettino said during the interval, there was little change after the restart as three goals flew in during a lively four minutes.
First, Sidibe headed home from close range after Mendy had left Winks for dead out wide but Tottenham were level almost immediately, as Alli was pulled back by Kamil Glik and, after a long hesitation, Dutch referee Bjorn Kuipers pointed to the spot.
Kane converted, his low shot too powerful for the outstretched hand of Subasic — but no sooner had the visitors equalised than they found themselves behind again.
Monaco needed only four passes from kick-off to unlock their opponents and again it was both full-backs involved, this time Sidibe supplying the cross for Mendy to drive home at the back post. Pochettino swivelled on his feet in frustration.
After taking five years to get back into the Champions League, they are out of it within three months.
Subasic, Sidibe, Glik, Jemerson, Mendy, Fabinho, Bakayoko, Lemar (Joao Moutinho 81), Bernardo Silva, Falcao (Raggi 89), Germain (Carrillo 77).
Lloris, Trippier, Dier, Wimmer, Rose, Alli, Wanyama, Dembele (Eriksen 65), Son (Janssen 64), Winks (Sissoko 76), Kane.
Bjorn Kuipers (Netherlands).