Swansea City lurk three points behind and are at home to relegated Stoke City, but they need to win and make up a 10-goal swing to escape the drop.
And Melchiot has warned his former club to act quickly in order to give the players peace of mind ahead of next season. They have two games at home.
Conte, who will attend Andrea Pirlo's testimonial on 21 May, suggested he was in the dark as to Chelsea's end-of-season plans.
Kane curled in the victor from the edge of the area in the 50th minute for his 28th league goal of the season, leaving the striker three behind Liverpool forward Mohamed Salah in the race to become the Premier League's top scorer.
Sunday's opponents Newcastle United (11-8-18) go into the match on the back of four straight defeats - a series of results that occurred immediately after the club passed the 40-point mark to effectively seal their Premier League status for another season.
The Reds have a far superior goal difference to Chelsea, who are two points behind.
Wednesday night's 1-1 draw with Huddersfield Town ended that winning streak and saw Tottenham guarantee their spot in the top four, but Chelsea could still catch Liverpool this weekend with a win at Newcastle and a Liverpool loss against Brighton.
"If you want to stay the same level as the previous year, you can stay in a comfort zone". People said that lineup was not good, but we won. We would get changed at Leeds Road, our home before we moved to what is now the John Smith's Stadium, and walk down the road to the local playing fields to practice.
The three teams going down are Stoke, West Bromwich Albion and, nearly certainly, Swansea.
City has now racked up 105 goals and 97 points to beat Chelsea's hitherto records of 30 wins, 103 goals and 95 points.
He added: "If you remember, last season after 10th place we won".
Chelsea fortuitously equalized in the 62nd when Mathias Jorgensen's clearance cannoned off Chelsea defender Marcos Alonso's head and went back into the net. "This was definitely the most important save in my career, no doubt about it", the 29-year-old Lossl said.