Chelsea had the chance to re-open a seven-point lead over Tottenham at the top of the Premier League by beating United at Old Trafford, but goals from Marcus Rashford and Ander Herrera in either half meant the gap stayed at four with six games to play.
The visitors were left frustrated by the first goal, though, with Chelsea claiming Herrera had handled in the build-up.
And boss Conte pointed to what he felt have been contentious decisions against his side in matches with Stoke City, Crystal Palace and Bournemouth.
"Last game against Bournemouth we conceded a goal in a same situation, against Palace a clear handball, against Stoke a penalty with great doubt. This is not important," Conte told BBC Sport.
"It is important to find the right solution, but the decision of the referee [Bobby Madley] wasn't good for us. We were unlucky."
However, Conte suggested the reason Chelsea lost was due to his failure to properly motivate his players against United, who they had already beaten in the league and FA Cup this season without conceding.
"I think that they deserved to win," he added to Sky Sports.
"They showed more desire than us and more motivation, but in this case the fault is the coach.
"It's [my fault], because in this case I wasn't able to spur the right desire or motivation to play this kind of game.
"To play this type of game from now and until the end we must have great enthusiasm, great motivation to try to reach the target."
Meanwhile, Manchester United midfielder in question, Herrera, has insisted team-mate Rashford's goal deserved to stand.
"I didn’t want to touch the ball with the hand," Herrera told Sky Sports.
"I was running with my hand next to my body.
"If you don’t have the intention to touch the ball and your hands are in a natural position it is not a handball."
While, Chelsea's lead at the start of April was 10 points, two defeats in four league matches has seen Spurs – who have won seven straight top-flight games – eat into that advantage.
And Conte admits he is worried by Spurs' form.
"For sure, I have concern because we have to work together and find quickly the right ambition to win this title," he said.
"If someone thinks it's normal for Chelsea to win the title, we started as underdogs after 10th place last season.
"Tottenham is in good form and playing with enthusiasm, we must find the same."