The Blues racked up another three points on Saturday, edging past struggling Swansea City 1-0 at the Liberty Stadium thanks to Cesc Fabregas' fourth-minute goal.
The win moves them two points behind Mauricio Pochettino's side, who host Watford at Wembley on Monday, and Conte remains cautiously optimistic that they could yet leapfrog their rivals.
He told BBC Sport: "The only way we can 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."
Despite not adding to Fabregas' early goal, Chelsea were in control throughout against the Swans.
Conte, though, wants his side to develop the habit of scoring when on top – something he believes they have not done enough this season.
50 - Antonio Conte has now won 50 of his 73 Premier League games as manager; only Jose Mourinho (63) and Pep Guardiola (69) reached 50 wins quicker in the competition. Esteemed. pic.twitter.com/aUVGhHfN5p— OptaJoe (@OptaJoe) April 28, 2018
"We started the game very well and dominated the game in the first half," he added.
"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.
"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."