The Hammers picked up a first home point and first clean sheet of the season during the goalless draw at the London Stadium, while also becoming the first team to avoid defeat against Chelsea this term.
However, West Ham squandered a number of chances to win the game, including one particularly glaring miss which saw Andriy Yarmolenko head wide of the target from close range.
"Maybe it seemed easier to score than miss. Maybe he relaxed a bit more," Pellegrini told reporters.
"It's a first clean sheet, against a team who have scored 14 goals, so in that respect I'm happy.
"But when you have chances against big teams you must score them. The draw is not a bad point but if we took those chances we could have got three."
West Ham now turn their attention to an EFL Cup clash with Macclesfield Town on Wednesday.