Spurs took five years to return to Europe's premier tournament but crashed out within three months after a 2-1 loss to Monaco ended their hopes of progress from Group E.
Goalkeeper Lloris, who is considering whether to extend his contract at White Hart Lane, underlined his importance with another excellent display at Stade Louis II, which included saving a first-half penalty from Radamel Falcao.
The Frenchman, however, could not prevent a third defeat of the campaign and Tottenham will now drop into the Europa League, provided they take at least a point at home to CSKA Moscow next month.
"It makes for a lot of frustration, I can't hide that," Lloris said.
"We will talk between ourselves and try to find solution
Maybe we are not ready to manage Premier League and Champions League campaigns at the same time, but we need to question ourselves about that.
"Everyone at the club was excited to play this competition, and all the players too, but we failed all together
We had bigger expectations in this group stage
We will not go through, we are still fighting for a Europa League but it's not enough for a club like Spurs
It's a big disappointment.
"We need to digest this and look forward to the game at Chelsea on Saturday."
Pochettino perhaps paid the price for keeping one eye on the clash at Stamford Bridge, as he left Jan Vertonghen, Kyle Walker and Christian Eriksen on the bench.
Vertonghen's omission was the most surprising, given he was not carrying an injury, and it is possible Pochettino was preserving the Belgian, who will be the only available option at left-back this weekend.
Danny Rose, who started in France, will be serving a domestic suspension and Ben Davies is out with an ankle problem.
"It is a question for the manager," Lloris said
"We know we have a good squad and sometimes it can happen that the manager rotates, but that kind of thing shouldn't affect the team because we have enough quality in the squad."
Injuries to key players have certainly hindered Tottenham's performances but it was consecutive home defeats at Wembley that damaged their chances most.
The club sold out for both matches at the 90,000-seater stadium, but it remains to be seen how many supporters would turn out if Spurs return there in the Europa League.
"It's a big honour to play at Wembley as the atmosphere is so amazing," Spurs defender Kevin Wimmer said.
"White Hart Lane is our home ground and everyone is comfortable there but if we play Europa League, it doesn't matter where we play as we want to show we can play in every stadium."
Source : PA
Source: PA