The Hammers grabbed a battling point at Chelsea on Sunday, in which Hart impressed, to give themselves a healthy six-point cushion above the relegation zone.
For much of the first half, the east Londoners did look second best, with Chelsea seemingly more risky with every attack.
"I think with this game we can see our season", Conte told the BBC.
Chelsea's persistent pressure eventually paid off thanks to Azpilicueta who prodded the ball home from close range after Morata headed back across goal from a corner.
Three times before at Stamford Bridge Javier Hernandez had been used as a substitute and the Mexican had scored on each occasion.
There was also a minute's applause prior to kick-off, with the Chelsea players wearing black armbands in memory of Wilkins.
Marcos Alonso nearly spared Chelsea s blushes with a thunderous strike, but Hart finished as West Ham s hero with superb saves to keep out that effort and one from an Olivier Giroud header. He doesn't cause problems, he can be angry but for five or ten minutes, no more than that. "I like to continue to say: "We have to work and improve".
"I thought we played against really slick Chelsea team in the first half", said Moyes.
"Like the last weeks again, we [gave] them a gift".
"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". A phenomenal recovery challenge from N'Golo Kante prevented the goal - and led to a fizzing shot from Hazard on the break within 15 seconds.
'The thing is we have to look we have start to play good football and win games.
West Ham's sporadic attacks were however Moore risky, and restored to the side skipper Gary Cahill had to be at his very best to thwart Marko Anoutovic, on 15 minutes.
"Two seasons I was in the away end celebrating with them, but this time I was out there playing, so it was a special moment". "At my angle I was waiting on Marko getting his shot away", he added. As the ball bobbled limply into the bottom corner the Hammers players stood and stared at one other, stunned by the shoddiness of their own defending.
"We will fight and give everything for the three points which would help us get out of the relegation fight completely".
"You must win this game if you want to reach a target, in this case we want to reach a place in the Champions League". He showed that performance. That will be good for Joe today.
Joe Hart admits West Ham face a season-defining game against Stoke next week and insists he is not thinking about this summer's World Cup.