Ben Chilwell was sent off for Leicester with 20 minutes left after a foul on Moses earned him a second yellow card.
The result represented the first time Chelsea have drawn three straight matches 0-0 in their history, and Conte blamed fatigue rather than singling out the misfiring Morata.
"We played with nearly the same players as against Arsenal. But I think I saw a lot of players very exhausted", Conte said.
Asked about Mourinho's "contempt" comments following Saturday's goalless draw with Leicester, Conte said: "I think that I said (I'd) stop the story".
Having been in charge at AC Milan he knows what it takes to manage amid great expectations and is committed to a brand of attacking football admired by Chelsea owner Roman Abramovich.
"I don't think it is only Morata's problem, also the other players, because we are not scoring goals, we are not conceding, but we are not creating chances".
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Ten-man Leicester produced an outstanding display to earn a point at third-placed Chelsea - although they should probably have come away from Stamford Bridge with all three.
Conte said: "We are talking about a top player in a moment when you can buy him with a price not so high".
- Leicester had 12 shots in the first half - the most of any visiting team in the opening 45 minutes of a Premier League match at Stamford Bridge since 2003-04. But it's something that we are thinking about a loan until the end of the season.
"Because I don't behave as a clown on the touchline, it means that I lost my passion", he said. I never see this type of mistake in the Premier League before. I understand Southampton are unhappy like I was not one time, more than one time when the mistake is against us.
Son Heung-min put Tottenham ahead in the 26th minute, courtesy of another close-range strike, and produced possibly the highlight of the game with his spin and driving run to set up Kane's first goal.
Swansea City remain bottom of the table as they drew 1-1 at Newcastle United.