Manchester United scored three goals in the final seven minutes against Everton to seal an emphatic victory.
But with the score at 1-0, De Gea made a number of fine saves, including from Wayne Rooney, who was playing against United for the first time since leaving at the end of last season.
Romelu Lukaku did manage to net against his former club, with goals also coming from Antonio Valencia, Henrik Mkhitaryan and Anthony Martial.
But Souness says the United players should thank De Gea for keeping them in front.
“United will look at that game and will talk about the goals,” he said.
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“Lukaku scored against his old team, the wonder goal of Valencia.
“But it’s games like today, I’m sure the manager and the staff in there are saying ‘by the way, you owe it all to this man here that you won 4-0’ and pointed to David de Gea.
“At 1-0 they were very much in it Everton, they started to dominate a lot of the ball in the second half.
“He makes a couple of saves that really he’s not entitled to make.
“Wayne will be kicking himself that he’s not put his one away.
“Sometimes goalkeepers are forgotten in the bigger picture, ‘oh 4-0, another 4-0 win’.
“But Manchester United’s goalkeeper today was as responsible as anyone for that result.”