The result left Leeds in a perilous position in the relegation zone going into their final game of the season at home to Tottenham Hotspur next weekend.
They trail 17th-placed Everton by two points, and are one ahead of fellow strugglers Leicester City, who have two games remaining.
Leeds led in the first half thanks to Rodrigo’s goal as they put crosses into the West Ham box and looked to pick up the second ball, but were below par in the second period and might have lost by a greater margin.
"We have to look at ourselves and say if we do win next week and do miraculously stay in the league, we have a long way to go in terms of quality in the squad," Allardyce told Sky Sports.
"The first XI really show up but when we needed that squad, they haven't quite shown the impact. I may be being unkind to them but it is only what my very experienced eyes are seeing at the moment.
"We have to keep going, we have to lift the spirits for next week, they have to accept the criticism, it is constructive criticism."
Allardyce was pleased with a strong first half showing on Sunday as Leeds went into the break level at 1-1 but having lost striker Patrick Bamford to injury before the break, they had nowhere near the same fluency in the second period.
"First half opportunities galore but not enough quality. Second half we needed to defend better and wait for our opportunities to take but unfortunately that wasn't the case.
"The West Ham players showed better ability in the final third than we did."
Allardyce is unsure whether he will have Bamford for the do-or-die visit of Tottenham.
"I won't know until he has had a scan. If it is his hamstring, perhaps unlikely," he said.
(Reporting by Nick Said; Editing by Toby Davis)
