The France international remains a Manchester United player despite the club-record signing being linked with a move to La Liga giants Real Madrid and Serie A champion Juventus this summer.
Pogba fuelled speculation in the summer transfer window by admitting that he would be open to a new challenge following three largely disappointing seasons at Old Trafford.
The 26-year-old has struggled to justify his £89m price tag since his return to Manchester United from Juventus in 2016.
Pogba won the Europa League and the League Cup in his first season back at Old Trafford but Manchester United have failed to win a trophy in the last two campaigns.
Former Liverpool FC midfielder Souness was quick to point the finger at the Manchester United midfielder.
“If I’m sitting in United’s dressing room, I’m glad Lukaku has gone and don’t want Pogba in there with me either if he’s not up for the fight ahead and is also keen to get away,” Souness told the Times.
“They’re as responsible as anybody for the predicament United are in, yet have effectively said to their teammates: “It’s everybody else’s fault.”
“No, let’s get it right, lads, you’re part of the reason United are not in the Champions League this year.
“Madrid are looking to nick Pogba on the cheap because they’re suspicious of his form, while Inter haggled over the asking price for Lukaku because he didn’t pull up any trees at United either.
“Instead of them taking the responsibility as senior players, that burden instead falls on Marcus Rashford at 21, and I’m not convinced he’s ready for it yet.”
Manchester United signed Swansea City winger Daniel James, Crystal Palace full-back Aaron Wan-Bissaka and Leicester City defender Harry Maguire in the summer transfer window.
The Red Devils will be eager to improve upon their sixth-placed finish in the Premier League last term to miss out on Champions League football.
Manchester United will compete in the Europa League for the second time in three seasons.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news