Kane, who is skipper of the Three Lions, was on the scoresheet twice to ensure a last-gasp win over their opponents in England's first game of the competition on Monday.
It had looked as though they were going to be frustrated by a defensive-minded Tunisian side, who had equalised from the spot after a dubious foul committed by former Spurs defender Kyle Walker, but Kane was on hand to nod home the winner in stoppage time.
Kane said: "I'm really proud of the players. We've done a lot of work on the training field and playing last we have seen a lot of games, so we've all been itching to play and it was tough.
"The World Cup is tough, especially the first game so it is good to get the nerves out of the way and excitement and then it was about trying to play and I thought we did really well, so I'm so proud of everyone."