Suarez returned from a ten game suspension last night in his side's 1-0 defeat at the hands of arch rivals Manchester United at Old Trafford.
The Uruguayan looked in good form and combined well with Sturridge and a new formation from manager Brendan Rodgers could allow him to get the best out of his strikers.
"They played a different system; it worked to a certain extent. Suarez and Sturridge's partnership looked sharp and together, and the formation looked like it could get the two of them to play," said Carragher on Sky Sports.
"But once you go out of the cup to Manchester United I don't think you should be looking at it and saying 'Liverpool played well... we did this well.'
"Every time the ball comes to Suarez's feet you think something special is going to happen, he was a big positive - but that's something you look back on in a few days time when you look at the positives.
"I agree with Brendan Rodgers that three at the back worked. Early on, Sturridge and Suarez up front looked like a good partnership."
The loss at the hands of United was the Red's second on the bounce after losing 1-0 at home to Southampton at the weekend.
Liverpool's playmaker Philippe Coutinho missed the games through an injury, which he suffered against Swansea, and Carragher believes once he comes back to action Rodgers may settle on the new formation.
"If you bring Philippe Coutinho in behind that front two in that formation - that could be the way he goes eventually because he's got that many centre backs. At the weekend he played four of them," said the former Liverpool defender.
"To get them in he may need to go three at the back, then you get your two up front, Coutinho in his position - it may be a really good formation for Liverpool.
"I think to a certain extent it worked tonight, but when you lose to Man United for me it's not important."
The 26-year-old striker scored 30 goals in 44 appearances for Liverpool last season and will appear in the league for the first time this season when his side travels to Sunderland.
Liverpool's defeat means they will only play Premier League games until the FA Cup begins in January.
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