The goalkeeper was highly impressive in the first encounter, with a dominant display earning his side a replay at Upton Park on Tuesday.
He was equally on form in that game, with one big save to deny Christian Benteke keeping the score tied at 1-1 late on before his side secured a 2-1 win courtesy of a header from Angelo Ogbonna.
And James says he deserves praise for his display again, believing that the Hammers number two has excelled when called upon.
“You’ve got to say well done to Darren Randolph once again,” he told BT Sport after the game.
“He was man of the match in the first game and then that massive save at 1-1 allows West Ham to go on and win it at the death. He’s done fantastically well.”
Randolph will now be hoping that he can keep playing a big part as his side eye a long run in the competition.
West Ham now face Blackburn Rovers at Ewood Park in the fifth round and will be confident of progressing against the Championship side, who have their attention elsewhere given their precarious position in the league.
Randolph will likely be in the team, and will be keen to replicate his displays from the Liverpool games to help his side progress once again.