Sunday's performance comes amid mounting speculation around Moyes' future at West Ham, after media reports this week that the East London club has contacted potential replacements.
"The manager should always take the responsibility, that's what happens when you do this job... Somewhere along the line the players have to take responsibility, do their jobs and be hard to play against," Moyes told reporters.
Asked about his future, Moyes said he would speak to the board at the end of the season, when his current contract expires, despite having already been offered an extension earlier in the season.
The defeat was the second consecutive away game in which West Ham conceded five goals, and David Moyes rued his side's defensive performance.
"We've not been able to do the basics defensively to give ourselves the chances to stay in the game," he said.
West Ham struggled to get into the game on Sunday, falling behind in the 15th minute as Cole Palmer pounced on a poorly-cleared cross.
The Irons went into halftime trailing 3-0, after goals from Conor Gallagher and Noni Madueke extended Chelsea's lead.
A second-half brace from Senegal international Nicolas Jackson sealed the result for Chelsea.
"I actually thought in the second half at least we made it hard for them to score. Two terrible goals, notwithstanding what happened in the first half," the Scotsman said.
The visitors did have a handful of chances - England international Jarrod Bowen hit the bar twice in the first half and once again in the second half.
It has been a frustrating second half to the season for West Ham, who sat in sixth place in December at the halfway stage, but have won just three league games out of 17 in 2024.
"We've not been in as good form since the Africa Cup of Nations," Moyes said.
"But I do think that we put in some really good performances in the early part of the season," he added later.
Sunday's defeat all but ends West Ham's hopes of European qualification next season - now sitting in ninth on 49 points.
"We don't want to fizzle out," Moyes said of the remainder of the season.
West Ham host Luton at the London Stadium next Saturday, before a final day journey to the Etihad Stadium on the 19th of May to face reigning champions Manchester City.
