Everton manager Ronald Koeman admitted his side did not deserve to get anything as they went down 3-2 against Spurs.
Kane and Lukaku began the day tied at the top of the Premier League goal-charts, and the pair took centre stage again as Kane’s double put Spurs two up before Lukaku’s late strike sparked hopes of a comeback.
Dele Alli restored the two-goal cushion in injury-time before substitute Enner Valencia added another goal seconds later to complete a dramatic finish at White Hart Lane.
Victory for Mauricio Pochettino’s men means they reduce the gap behind league leaders Chelsea to seven points, with the Blues travelling to West Ham on Monday.
Kane slotted his second of the game after Joel Robles rolled the ball out to Morgan Schneiderlin, who was dispossessed after a misunderstanding with Ashley Williams.
“We did some mistakes and if you make those kind, like the second and third goals, it was too easy,” said Koeman.
“We did well. We had some good counterattacks but needed more composure on the ball. We had the chance to get a point but it was not deserved.
“Tottenham have two or three years in a row with the same players, it’s all about time which is what we need to have,” he added.
“If we get the time to improve, that’s the next step for the club.
“Romelu Lukaku showed again he’s so strong and dangerous and if he gets a chance it’s a goal,” Koeman continued.
“It wasn’t a competition between the strikers – but he and Harry Kane both showed their quality of finishing.”