The lead, however, lasted 90 seconds before the impressive Riyad Mahrez equalised with a superb curling effort.
Having lost 1-0 at Manchester United on the opening day of the season, Tottenham have collected just two points from three matches and sit 15th in the table.
"I am angry and disappointed, not frustrated," Pochettino told the BBC. "The mistake (of conceding after scoring) we made today is difficult to explain.
"I am disappointed with the draw. Last game against Stoke we lost a 2-0 lead and we did it again. We deserved more again but it is a shame.
"We need to work hard to be more focused and more aggressive after we score because this is the second game we concede the draw when we deserve more."
Striker Harry Kane cut a forlorn figure for much of the game while Spurs lack of creativity was horribly exposed in the absence of playmaker Christian Eriksen with a knee injury.
Argentina forward Erik Lamela replaced the Dane but he was largely ineffective and Pochettino said before the game that the need to add more support up front for Kane, who netted 31 goals in all competitions last season, was "obvious".
Leicester maintained their Premier League status with a stunning run of form last season and have carried that momentum into the new campaign under new manager Claudio Ranieri.
Led by exciting Algeria winger Mahrez, Leicester top the fledgling table with seven points from three matches.
"I am happy, My players have a fantastic spirit," said Ranieri. "It was an outstanding goal and Riyad Mahrez is a very good player. Skill makes the difference and Mahrez has very, very good skill."
Despite an impressive start, however, the Italian said preserving their top flight status remained paramount.
"It is important to maintain our place in the Premier League. Seven points, 33 less (than the perceived 40 point safety line), that is important for us."
(Reporting by Tom Hayward; Editing by Ken Ferris)
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