Hamann: Time for Reds to step up
Carroll is fast approaching the first anniversary of his club-record £35million move from Newcastle and, while injury delayed his start, he has scored only six goals in 33 appearances.
Downing moved from Aston Villa for £20million in the summer but his only goal in 24 games came in the last minute of the 5-1 FA Cup win over League One Oldham.
The Reds have struggled to beat sides at Anfield, where they have drawn seven of 11 Premier League matches this season, and in the absence of the suspended Luis Suarez Kenny Dalglish's side seem to be missing a cutting edge.
"I watched them on Saturday and they found it hard to create goalscoring opportunities," said Hamann, at an event at the Football League headquarters on Thursday ahead of next week's Carling Cup semi-final second leg between Liverpool and Manchester City.
"For a team that wants to finish in the top four, they didn't create enough.
"In previous games they have created but couldn't score and they have found goals hard to come by.
"Steven Gerrard was the top goalscorer on the pitch for most of Saturday's game and he has missed more than half the season.
"The likes of Downing and Carroll have to come to the fore now and start producing the goods because they are there to create chances and score goals and so far they haven't done it.
"I still think both can be very good Liverpool players for years to come but at some stage you have start performing and start scoring goals.
"Carroll came on on Saturday and the crowd gave him a rousing reception and people and fans still back him.
"I feel it is time for him to step up and start giving back some of that belief and faith that the club showed in him in splashing out £35million on him.
"If you don't score and you cost a lot of money you get stick but I think he is big enough to deal with that. Kenny has kept faith in him but he has to step up now with Suarez out - the goals have to come from somewhere.
"Kenny keeps backing him, as the fans do, so he has all the support he needs.
"He just needs to start performing and scoring goals."
Hamann believes despite both players being England internationals, Downing with 32 caps and nearly seven years' experience with the national team, they still require a period of adjustment.
The pair may still be in that settling-in period but the former German international is confident they will make the step up.
"At other clubs if you perform two times a month sometimes that is enough but at Liverpool you have to do it every four or five days," he added.
"You are playing for a bigger club and you have to perform on a regular basis - every single game you have to prove yourself.
"There is a difference (being at Liverpool) but they have been here for a few months, they are English players who have played in the Premier League for a number of years and I don't see the reason (why they have not been successful)."