Kane missed the chance to draw England level when he skied the second of two penalties which saw the defending champions scrape through to the semi finals at England's expense.
The 29-year-old looked distraught after the game and Lloris, whose presence in goal seemed to have destabilised the prolific frontman, has revealed he had a difficult chat with his club mate afterwards and is optimistic he will bounce back stronger.
"I don't need to go too much further," Lloris said.
"We texted after the game. It was not easy to find the words straight after, in the changing room. I think he needed some rest.
"It's a difficult time for the English national team and for Harry, but I think he can be proud of what he's done for the team during this World Cup.
"In football history, many top players missed important penalties in their career – like Leo Messi, Cristiano Ronaldo and Kylian Mbappe.
"I've no doubt he will keep his chin up, and he will have Tottenham and the national team to shine [for]."
Kane's first goal from the penalty spot saw him join Wayne Rooney as England's joint all-time top scorer with 53 goals.
