The Hammers' winless run in the Premier League extended to six games as they were dealt a 3-0 beating at Turf Moor.
The final blow came early in the second half when goalkeeper Roberto inexplicably pushed Ashley Westwood's corner into his own net.
The Spaniard was under-fire from the away support for the remainder of the match, but Pellegrini is reluctant to seek scapegoats.
"I never make individual analysis here in the press conference," he told the assembled media, including VAVEL. "It's the responsibility of all of us."
Pellegrini bemoans 'easy goals'
The Chilean claimed that the three goals resulted from the visitors' failings than from bright Burnley attacking play.
He also suggested that his team are lacking focus when defending set-piece situations after their opponents twice scored from dead-ball situations.
This had also proven their undoing in their 3-2 home defeat to Newcastle United last weekend.
"It's difficult to analyse the performance when you concede such easy goals.
"It's very difficult when the other team scores goals that are not made from their play, just from our individual mistakes.
"[Set-pieces are] one of the big problems that we are having.
"Of course, it's very concerning that we are having so many distractions. Newcastle was the same, Crystal Palace was the same."
A response after the international break?
West Ham have now fallen to 16th in the table and the list of upcoming fixtures appears far from favourable.
Though he is under increasing pressure, Pellegrini remains optimistic.
"You never know in this league which are the more difficult games and which are easy.
"I hope that in these 14 days, we are going to work and see what happens in the next game."
Noble and Lanzini updates
Pellegrini confirmed that Noble, who was able to walk off the pitch, albeit very gingerly, had twisted his ankle.
Lanzini, however, had to be stretchered off after injuring his shoulder, and the club face a nervous wait to discover the extent of what may well be a serious problem.