Guus Hiddink's side fell behind to Manuel Lanzini's superb strike before Cesc Fabregas curled home a delightful free kick to level the score on the stroke of half time.
The Hammers went in front for a second time on the hour mark when Andy Carroll slotted home but Chelsea rescued a late point in the last minute thanks to a contentious Fabregas penalty.
Michail Antonio appeared to foul Ruben Loftus-Cheek outside of the box but Willian is adamant his side should have been worthy winners, despite only narrowly avoiding their fifth home defeat this season.
"I think we deserved to win," he told the club's official website.
"We played well, especially in the second half. In that moment we played very well and they scored a second goal.
"We continued to play and we created so many chances to score more goals but we didn’t."
Chelsea remain unbeaten under Guus Hiddink but currently occupy 10th place in the table, with their hopes of a top-four finish all but over.
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Willian has admitted the club's failure to fight for silverware is difficult to take, but remains adamant Chelsea cannot take their foot off the pedal during the run in.
"We fought until the end and we have to continue in that way in our remaining games.
"It is difficult when you don’t have chances to win the title, but we play for Chelsea, and we have to continue to play to the end," he added.
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