Kante returned to action as a half-time substitute against Spurs after missing the west London club's previous two matches with an ankle injury he sustained during Chelsea's 1-1 draw with Liverpool last month.
Second half goals from the French midfielder, Thiago Silva and Antonio Rudiger sealed a comfortable 3-0 win for the Blues as they continued their unbeaten start to the season in all competitions after six matches.
The 30-year-old World Cup winner believes that Sunday's win was down to Tuchel's message at half-time, but explained that they haven't won anything yet.
'We received good advice from the manager at half-time, who told us to win more duels and play with more force. We had a super second half,' he told Chelsea FC.
'Last year gave us a lot of confidence but we know nothing is going to be easy and we need to work hard and work together. It is important that we started well this season but there are many important games and we need to carry on.'
'It wasn't my most beautiful goal, but it was an important goal and it helped my team. Mateo [Kovacic] gave me the ball, I saw that I had time to shoot so I shot, it was a deflection, but I am happy that it touched the post and went in. I am happy that I helped the team.
'I am feeling better. I think we managed the injury very well. I took time to come onto the pitch and I am happy to be back and I felt very good.'
Meanwhile, the German head coach was full of praise for Kante on his return to the side.
'He's a top player. If you have N'Golo, you have something everyone is looking for. He is a unqiue guy. He is fantastic,' he told BBC Match of the Day.
Chelsea will be hoping to continue their almost perfect start to the new season when they play host to Aston Villa in the Carabao Cup on Wednesday, before a match against current Premier League champions Manchester City at Stamford Bridge on Saturday.
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