"We need to talk a lot between us and the club", said Pochettino.
Leicester were great value and played their part, having led 3-1, with two goals for Jamie Vardy and one apiece from Riyad Mahrez and Kelechi Iheanacho.
Lamela inspired the fightback by twice finishing from Kyle Walker-Peters assists, and it was the Argentine's strike that forced an own goal from Christian Fuchs to put Spurs in front by the hour mark.
However, their lead lasted less than three minutes when Lucas Moura won the ball high up the field from Danny Simpson and fed in Harry Kane, who slotted the ball past Eldin Jakupović in the Leicester net.
It remains to be seen if boss Mauricio Pochettino and key centre-back Toby Alderweireld, who have both been the subject of speculation surrounding their futures, will remain with Spurs when they leave the national stadium to play at their new ground on the site of the old White Hart Lane next season. @HKane cuts inside his man and curls a lovely effort into the far corner to score his second of the afternoon! We need to think our reality is different and our fans need to think and be happy and support us because we are not a club who will spend insane money.
Vardy then made it 4-4 as Mahrez timed his pass perfectly and Vardy smashed home his 20th goal of the PL season in style.
Leicester's lead was at two for just two minutes.
Leicester and Tottenham contributed to a game which matched the all-time record for goals scored in a single match at Wembley, in a topsy-turvy game which did not appear to have little meaning for either side.
"From the beginning it was tough [playing home games at Wembley]".
Game over? No. Harry Kane had other ideas.
Kane, though, had the final say and bowed out on 30 league goals and it was a beauty, as he left Hamza Choudhury for dead and curled the ball into the far corner to end the match and Tottenham's Wembley stay in fine fashion.
"It's insane to lose a game where you've scored four goals away", Puel added.