The 'Blues' surrendered a one-goal lead to go down 2-1 at Old Trafford and now sit fifth in the Premier League table, two points behind fourth-placed Spurs with just 10 games of the season to go.
Speaking after the game, Conte admitted that the competitive nature of the Premier League means that it will be harder than ever for the 'Blues' to ensure Champions League qualification through the league.
"There is this risk," said Conte. "We must be ready to be concentrated, and to understand this target is an important target for us."
"In this league, getting a place in the Champions League is not simple.
"We are disappointed with the final result. We had a great chance to get three points against a competitor for a place in the Champions League, but in the end we are talking about another defeat.
"This country has the only championship where you can find six teams who start the season by fighting to win the title or getting a place in the Champions League."
Chelsea face Premier League pacesetters and nerly-crowned League Cup champions Manchester City next time out in what could prove to be a make-or-break game for their top-four hopes.