Conte bemused by Blues' failure to beat West Ham
The Blues dominated their opponents from start to finish and only wasteful finishing and superb goalkeeping by Joe Hart prevented them from adding to Cesar Azpilicueta's first-half opener.
Their failure to make their dominance count was punished 17 minutes from time when Javier Hernandez fired home just four minutes after coming off the bench.
Conte was at a loss to explain how his side failed to take all three points, but did seem to question his players' desire to capitalise on their complete control.
"It is very difficult to explain it," he told Sky Sports.
"We dominated the game and created many, many chances to score but we didn't and that explains our season.
1 - Chelsea failed to win a Premier League game at Stamford Bridge under Antonio Conte in which they led at half-time for the first time, having won each of their previous 18 before today. Halted. pic.twitter.com/VbUkG9IfeY
— OptaJoe (@OptaJoe) April 8, 2018
"We have had good performances all season but you have to score. This is not the first time and we have to improve a lot. When you stay in this position in the table it means that you have a problem.
"We have to improve, we must win this game. Instead we are talking about a draw.
"You need the desire to score a second goal, a third, a fourth."
Antonio Rudiger was equally frustrated with his side's inability to hold onto their lead and questioned why it has become a recurring theme of their season.
He added: "I think we begged for the goal, and in the second half, or even in the first half we could have finished the game, but like the last few months we couldn't, and we conceded at the end.
"It's not easy to explain, I don't understand after we go 1-0 up why we always drop off and let our opponents come onto us.
"We could have done better, of course, we gave them a gift, it was the first clear chance they had and they scored."