The Reds travel to Old Trafford on Saturday for a contest that pits second against third.
And Carragher believes Andy Robertson and Trent Alexander-Arnold can prove pivotal to their team's success against the typically negative United.
"You expect Mourinho will have a plan, as he did against Chelsea last week with Eden Hazard," Carragher told MNF Extra.
"So if the front three are nullified, where can Liverpool hurt them? I want to look at the role of the full-backs.
"There's definitely been a change at full-back. Not just in terms of the players there, with Robertson on the left side instead of Moreno, and Alexander-Arnold instead of Gomez on the right. But also the positions they're taking up - there's definitely been a change with Liverpool's full-backs.
"They're not as high and as wide as they were. And they're not going too early now.
"Before, you might see Alexander-Arnold on the touchline, even before the ball goes to Jordan Henderson. But there has definitely been a change and I think it has helped them defensively. Now they're coming onto the ball and arriving in that position, not waiting for the ball out there.
"That's what I like to see - taking the ball on the run, not standing there in wing positions. It's better defensively, too.