The Foxes moved level on points with Arsenal at the top of the Premier League table thanks to Robert Huth’s 83rd-minute winner at White Hart Lane.
Kane came close for the north London side but the England striker’s attempt was touched onto the woodwork by Leicester goalkeeper Kasper Schmeichel.
Tottenham are seven points behind Arsenal and Leicester following their second defeat of the season at The Lane.
But Kane urged his Tottenham team-mates to stick together ahead of their next game against Sunderland at home on Saturday.
Tough defeat to take. We're together as a squad & we'll be back at the Lane on Saturday to put it right. pic.twitter.com/m8scmDnbNa
— Harry Kane (@HKane) January 13, 2016
Leicester centre-half Huth, who moved to the Foxes from Stoke City in 2014, could afford a joke at his own expense after his headed winner against Tottenham.
It's not often having a square shaped head comes in useful!! #lcfc
— robert huth (@robert_huth) January 13, 2016
Leicester face Aston Villa in their next Premier League game before hosting Spurs in their FA Cup third-round replay next week.
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