The young Reds fell behind just two minutes into the Premier League 2 encounter on Sunday but recovered quickly and went on to create a host of opportunities.
However, a combination of the determined goalkeeping display by Hammers stopper Nathan Trott and and their missing several big chances cost Critchley's team.
Matty Virtue did level for the Reds in Kirkby, but a superb free-kick from Oladapo Afolayan 17 minutes from time earned the visitors the three points.
"That was very hard to take because I think the least we deserved out of that game was a draw," Critchley told Liverpoolfc.