Llorente had a golden chance to equalise but blazed wide from close range as Pochettino's men went down to a 2-1 defeat at the King Power Stadium.
The former Athletic Bilbao star's form at Swansea City had Chelsea and Spurs in the hunt for his services during the last transfer window but he is now without a goal in 15 games since joining the north London club.
"Yes of course, it is about building the confidence of the player and, it is true, the chance was so clear," Pochettino told reporters afterwards.
"We feel bad because it was a chance to score for 2-2 and it was so clear.
"We need to accept that but everything in the last few games is against us and we need to be calm, trust and work hard for the next game."
Tottenham have only won once in their past five Premier League games, losing two of the last three, and travel to Watford on Saturday.