Sanchez has struggled for consistency since his move to Old Trafford from Arsenal in January, scoring just four goals in 25 appearances for the Red Devils.
Such form saw him dropped from Jose Mourinho's squad for the Red Devils' recent defeat to West Ham, while he has started just four of United's eight Premier League games this season.
Coming off the bench to score a stoppage-time winner against Newcastle last time out has seen some suggest that the Premier League's highest-paid player could be about to turn a corner.
But Carragher has his doubts over a player who has rarely had much time off in recent years - something he also believes happened with Torres ahead of his failed £50 million move to Chelsea from Liverpool in 2011, with the Spain international failing to hit the heights many expected of him at Stamford Bridge.
"There is broad agreement Alexis Sanchez has not been the same player since he joined Manchester United," he wrote in his column for the Daily Telegraph. "Actually, this is slightly inaccurate. Sanchez has not been the same player for longer than that.
"The more I watch him in a Manchester United shirt, the more convinced I am his poor final year at Arsenal was not due to a declining team or loss of motivation as he prepared to leave.
"Sanchez's best years have gone. He is to Manchester United what Fernando Torres was to Chelsea.
"The warning signs should have been clearer to Manchester United when they pursued Sanchez. The forward they signed had made 667 senior appearances for club and country before his 29th birthday.
"By any standards, that is a massive number. Copa America, Confederations Cup and World Cup commitments have stopped Sanchez enjoying a summer break throughout his career.
"The reports coming out of Arsenal during the final months of Sanchez’s spell at the Emirates were uncannily similar to those I recall about Torres at Anfield, his declining contribution attributed to a general malaise at the club as Arsene Wenger’s reign came to an end.
"No matter what the circumstances, no world-class footballer wants or tries to play badly. There had to be more to it, and Arsenal fans seeing Sanchez toil at United will be the least surprised at how the move is turning out."
Sanchez's disappointing displays have contributed to United's underwhelming start to the Premier League season, with pressure mounting on Mourinho as his side toil in eighth place in the Premier League having already suffered three losses in their eight games.
Supporters, though, have turned their attentions towards the club's board when showing their discontent, with executive vice-chairman Ed Woodward being blamed for the club's lack of transfer activity over the summer.
But Carragher feels Sanchez himself needs to shoulder some of the blame given that expectations were that he would spearhead United's pursuit of silverware and has thus far failed to pull his weight.
"There were reports that Sanchez is unhappy with his role at United under Mourinho, but the manager is entitled to be unhappy with how his marquee signing is performing," he added. "Rather than seeking to blame others, Sanchez should be looking at himself.
"Sanchez is the elephant in the room for Mourinho and all those United fans seeking to pin all the blame on executive vice-chairman Ed Woodward for the current imbalance in the squad, failing to secure transfer targets.
"When you hear and read some of the remarks about United’s poor recruitment, you would think Mourinho is the only manager in the world who has missed out on targets.
"Sanchez’s salary is reportedly the highest of any Premier League footballer and in the same ballpark as Lionel Messi and Cristiano Ronaldo.
"United thought they were signing a ready-made, world-class attacker who would immediately elevate the quality of their side – a guarantee of goals and assists. Instead, Sanchez is one of the many problems contributing to a difficult period in Manchester United’s history."
Sanchez will be hoping to be back among the United starting XI as they take on Chelsea on Saturday as domestic football returns following the international break.