Morata's goal was cancelled out by Christian Eriksen in the second half.
Ex-Tottenham midfielder Ryan Mason went on Twitter following Spurs victory against Chelsea at Stamford Bridge to have his say on the criticism Dele Alli had been receiving prior to his brace against the Blues.
Fourth-placed Tottenham, unbeaten in the league since December, began the day five points clear of Chelsea, but it looked like being a familiar tale of woe when Alvaro Morata punished a Hugo Lloris mistake to head the hosts in front on 30 minutes.
That was a fact the home fans weren't slow in reminding their visitors before kick-off of Spurs' 3-1 win on Sunday, as a huge banner declared Chelsea the "Pride of London". Even more impressively, Spurs did most of the damage without Harry Kane, who made his return from injury as a second-half substitute. Four years ago when we signed (at Spurs), the idea was to reduce the distance to the top four.
Spurs boss Mauricio Pochettino was delighted with Alli's display but feels he should be given "room to breathe" in his development.
Conte has consistently complained of his lack of input over transfer dealings this season and insisted he has got the most out of a squad that won the Premier League at a canter last season.
Asked if any chance of overhauling Tottenham had now gone, Conte said: "I don't know".
"The goal at the end of the first half it wasn't good for us and our confidence".
Aside from the visit to Chelsea for the penultimate game of their season, Liverpool have a potentially comfortable run-in with Bournemouth, Stoke and Brighton all to visit Anfield, and a trip to bottom club West Brom - although Alan Pardew's side did knock Liverpool out of the FA Cup.
The deadlock was broken in the 75th minute by Pierre-Emerick Aubameyang from the penalty spot after Bruno Martins Indi was penalised for fouling Mesut Ozil despite appearing to win the ball. I'm very exhausted for one season to repeat always the same things. He added, "He can't stand that they buy and sell players without consulting him".
"It just dawns on you sometimes: how many times does he make runs past the central striker anymore?"
A second capitulation in three seasons does not speak well of this group of players but, just as Jose Mourinho will forever be tainted by the torrid final months of his second Chelsea spell, Conte cannot escape blame for the current drift - particularly given his increasingly ludicrous pronouncements that neither he nor his team could possibly do better.