Pickford was pipped to the coveted Golden Glove award for the tournament's best goalkeeper by Belgium's Thibaut Courtois.
In his column for The Sunday Times, Souness wrote: "The statistics I saw said that Jordan Pickford kicked the ball 47 times in the semi-final - which is way too many - and in only 22 of those clearances did he find a teammate, which is way too few.
"My problem here is not really with the keeper but with those in front of him. Kyle Walker, John Stones and Harry Maguire were selected as the back three because they apparently had the skillset to play the ball out from the back.
"Yet when the pressure was on and they were pressed by the Croatians, they turned their backs on Pickford, forcing him to punt long. So often did they do this that the numbers on their shirts must now be indelibly etched on their keeper's mind.
"When we talk about bravery and defenders, we invariably mean the courage to challenge for the ball in the air or on the ground. It was bravery of a different kind that was required against Croatia, however.
"Where was the strength of character to demand possession, to have the nerve to bring the ball out and make the pass that helped England regain the initiative in the last half-hour of normal time or during extra time?"