The Reds thought they had won it in the final minute when Salah scored again, but Kane made amends for his earlier miss from the spot as he restored parity with a stoppage-time penalty.
Seven of Liverpool's last eight games have ended with more than 2.5 goals.
Roberto Firmino then went close midway through the first half with a header from Trent Alexander-Arnold's cross that drifted past the left post.
"There were so many situations to talk about but the ref's decisions decided the game so I can't help but talk about them", he told BBC Sport.
Harambee Stars Captain Victor Wanyama stepped off the bench to score barely two minutes on the pitch as Liverpool and Tottenham played to a 2-2 draw in Wembley. "Then for the softest touch of the whole game he decides it is a foul".
Replays showed the striker to be in an offside position when he received the ball, but the linesman's flag stayed down, ruling that the pass into Kane had come off Dejan Lovren. "You see him (Kane) diving clearly and no-one is talking about it but I think it is a dive", said Van Dijk.
As for Kane's century of league goals, arriving in such dramatic fashion, the Spurs manager said: "He is one of the best strikers and he was calm".
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Du Plessis shared partnerships of 74 with Chris Morris and 56 with Andile Phehlukwayo for the sixth and seventh wickets. When asked if he had suffered any injury while fielding, Du Plessis said, "Just a few battle scars".
Kane has claimed he will stay at the club - but wants to make sure he gets enough of a chance to develop his own skills and win the best trophies in football - something that Spurs now look incapable of being able to do. The referee didn't initially give the penalty, but was persuaded to change his mind by his assistant after a minute of consultation.
Liverpool have lost only one of their last seven meetings with Tottenham.
Defender Virgil van Dijk, returning to the Liverpool starting lineup, did a fine job of keeping an unchanged Spurs quiet for the majority of the first half.
Tottenham's only shot on target in the first 45 minutes came via the boot of Mousa Dembele, but his half-volley was easily saved by Loris Karius.
"Sometimes you complain about them, me no because I decided a long time ago to stop complaining about referees". I think nothing, to be honest. I was calm, because I think the team plays so well.
Liverpool offer so much that is good when it is measured in goals and excitement, but that nasty habit of carelessness and conceding crucial goals has still not been cured.
While Liverpool fans will doubtless want to remember this game for Mohamed Salah's brilliance, it will forever be tainted by two controversial penalty calls. "Sometimes you complain but, when they are right and show character, I think it is important to recognise and congratulate them, because they have a hard job". Chelsea is sandwiched between them, while Arsenal, boosted by two high-profile January signings in Pierre-Emerick Aubameyang and Henrikh Mkhitaryan, is four points further back.