Cesc Fabregas scored the games only goal, as Chelsea triumphed over Swansea in South Wales. Conte's side now sit in fifth, two points behind Spurs, in their attempts for Champions League football.
Despite picking up three points, the Italian expressed his unhappiness at his sides lack of clinical ability in front of goal. Chelsea had 11 shots on goal, and only three of them hit the target.
Conte told BBC Sport: "We started the game very well and dominated the game in the first half. But you must be very good to kill the game and you have to take the chances otherwise you risk your opponent trying to push.
"We were very good defensively and it's important for us to take three points with a good win. Now we have three games to go and have to win for our fans, for our work and then we'll see what happens.
"The big problem that we are having this season in many games is that we create many chances to score but we don't take them. If we want to fight for something important you must be clinical.
"If you don't kill the game then it's normal for the other team to push. Our expectation was to play a tough game against a good team looking to avoid relegation."
After this victory, Chelsea have all but secured, at the very least, Europa League football in fifth. However, Conte reminded us that his clubs aim is the top four, and this victory has put them with a positive chance of achieving this goal, however, Spurs still remain in charge of their destiny.
He added: "They only way that we have to put a bit of pressure on the top four is to win. Today has been very positive to put that pressure on Tottenham. Football is not simple and anything can happen."