Morata missed three one-on-one chances as Chelsea drew 2-2 with Arsenal, including a last minute opportunity to clinch all three points.
The agitated Frenchman will also have to pay a fine totaling £40,000 ($54,225) after being charged by the governing body for his conduct in the match officials' changing room following a 1-1 Premier League draw at West Bromwich Albion on New Year's Eve.
"I think it is a pity because when you have so many chances to score you must win the game", said Conte. He is not lucky in this period.
"Today he had chances but this is football".
"Petr (Cech) is a great goalkeeper, it is always hard to score against him but I put the ball in the net and that was the most important thing". He's very young, he has to continue to work, continue to improve.
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Morata, 25, fired well wide when sent through on goal early in the match.
Morata should have given Chelsea a last-gasp victor but Cech saved his effort when he only had the goalkeeper to beat before Davide Zappacosta crashed a shot against the crossbar.
The draw means Chelsea stay third in the table, a point behind second-placed Manchester United and 16 adrift of leaders Manchester City.
"Instead we are talking about a draw against a good team, but in this game we deserved to win as we created a lot of chances".