Lloris has been much-criticised this season as he admitted to a drink-driving charge in September and a series of errors in the Champions League have also cost Spurs on the field.
However, Pochettino has stood by the man who lifted the World Cup for France this summer.
“I am happy with him. (Players) are not machines, they can have an up or down,” said Pochettino. “Hugo is one of the best, there is no doubt.”
Foyth, 20, also showed impressive character to bounce back after conceding two penalties on his Premier League debut last weekend at Wolves.
“I was a centre-back and you are involved in this type of situations, but the confidence in him from the club, from us and his team-mates is massive,” added Pochettino.
“Today he showed great character, great personality to do so well.
“He’s so mature, (he) is a player for me that has all the potential to be one of the best centre-backs in Europe.”
Spurs show toughness
At the end of a gruelling run of five games in 12 days, Spurs were again far from their best.
But contrary to Tottenham sides of old, Pochettino’s current crop have shown a resilience to put a mounting injury list and uncertainty over when the club’s new stadium will be completed behind them, to keep grinding out results.
“It’s been a massive effort from the players and staff,” said Pochettino.
“Maybe the performance wasn’t the best, but the belief and fight was there. I’m so happy for that.”
Spurs were dealt an injury blow when Kieran Trippier limped off midway through the first half with a groin injury, but Pochettino is hopeful he could still be fit for England’s upcoming internationals with the USA and Croatia.
Palace were also missing star man Wilfried Zaha due to a hamstring injury.
The Eagles still haven’t won a Premier League game without Zaha since September 2016 and despite Palace boss Roy Hodgson insisting they could have won the game, the Ivorian’s end product was missed.
“I know we didn’t lose the game today just because Wilf wasn’t there,” said the former England manager.
“They took advantage from a corner with one of the very few chances they had, whereas we laboured away and didn’t take one of ours.”
Shorn of Zaha’s pace on the break, Palace looked most likely to score via a set-piece and James Tomkins headed wide when unmarked at the back post from Luka Milivojevic’s corner just after the break.
Yet, it was ultimately Palace’s own inability to defend a simple corner that saw them lose for the sixth time in their last seven games.
Foyth will have happier memories of his second Premier League start as he gratefully headed home from close range while Jordan Ayew dithered.
Palace did at least ensure a frantic finale as Jeffrey Schlupp’s shot from just outside the box forced Lloris into his first serious save.
Lloris also denied Andros Townsend in the closing stages, but his best save came from Sorloth’s near-post drive to keep Tottenham in the title hunt.