Kane hit a UEFA Europa League hat-trick and Erik Lamela fired in a couple of crackers as Mauricio Pochettino's side kick-started their Group C campaign at White Hart Lane on Thursday.
There was late drama as Spurs keeper Hugo Lloris saw red for bringing down Anastasios Tsokanis when he was clean through - and Kane, deputising in goal as Pochettino had already made three substitutions, allowed a Jeronimo Barrales free-kick to creep in.
"It was a great night until I went in goal," joked Kane in a post-match interview with ITV. "It wasn't the best effort and I'll leave that to the keepers from now on.
"I actually quite fancied myself in goal but when I saw that free-kick wobbling at me I wasn't too happy.
"It was a shame to let it in but overall it was a good game - it was a great result for us, a great win and I'm happy to get a hat-trick."
Kane's first goal was his best as he opened the scoring with a low, long-range effort which flew past Tomas Kosicky.
"It was a sweet strike," he added. "I knew it had a chance when I hit it and fortunately it went in off the post, which is always nice.
"It was obviously good to get the second and the third as well as we want to start killing off teams.
"Sniffing in and around the six-yard box is where it all counts too."
However, Kane was outdone by Lamela's outrageous, 20-yard 'rabona' strike that sent Tottenham into the break 2-0 up.
"I've seen him do that in training - he's got that in the locker," said Kane. "It's great for him to see it pay off on the big stage in a game."