Gerrard missed the last two and a half months of the season after a groin operation in March but did some work away from the main group as he continued his rehabilitation.
Carroll struggled for fitness after arriving in January from Newcastle with a thigh problem but he was involved with the rest of the squad.
Back in action: Liverpool players Martin Skrtel, Danny Wilson, Andy Carroll and Alberto Aquilani begin pre-season training
Defender Martin Kelly, whose season was ended by a hamstring in February, was also involved as was Daniel Agger, who was sidelined with a knee injury from early April.
Also training was Alberto Aquilani, back at the club after a year out on loan at Juventus.
The Serie A club did not take up their option to sign the Italy international and although he has returned to Merseyside he is thought to be one of a number of players manager Kenny Dalglish is looking to offload to free up space on the wage bill to bring in more new signings.
Also believed to be on that list are Christian Poulsen and Joe Cole and they too were put through their paces in the sunshine at Melwood.
Vice-captain Jamie Carragher is keen to pick up where last season left off.
'We've had longer than usual off this year and I want to get started now,' he said. 'It's a new start and there's a new sense of optimism. It's going to be great to have most of the players around from the start of pre-season.
Champing at the bit: Jamie Carragher is keen to get started
'Our form in the second half of last season was very good and we need to ensure we prepare well and get off to a decent start this season.
'That will make a big difference. It can be difficult with the preparations when everyone comes back in dribs and drabs.
'It's good for the manager to have everyone around and it means after a decent pre-season we should be ready to start the season.
'It will be great to see all the lads again and I'm sure there will be a few new faces coming in before the transfer window closes.'
New ?16m signing Jordan Henderson was absent as he was given extended leave having been involved with England Under 21s at the European Championships last month.
However, one new arrival out on the training ground was coach Steve Keen, appointed to the backroom staff yesterday, getting up to speed with manager Dalglish and first team coach Steve Clarke with director of football Damien Comolli also watching from the sidelines.
'I feel really privileged, proud and honoured to be here and to be part of such a fantastic club,' Keen told liverpoolfc.tv.
'In my eyes Liverpool are one of the greatest clubs in the world so I am really quite humbled to be here.
'I was back coaching at West Ham for nine years and was a player at West Ham for nine years as well, so they have been a big part of my life but when I got the call from Liverpool I thought the timing was perfect for me.
'To come here and be a part of what Kenny, Steve Clarke, Damien and the owners are looking to do in taking the club forward is very exciting.
'I know Steve very well from my West Ham days and learnt a lot from him when he was assistant manager to Gianfranco Zola.
'He's very meticulous with his planning, he's a fantastic coach and a really nice person to work with. I want to come in here and to contribute to us winning trophies for the supporters.
'We've a lot of work to do between now and the first match of the season against Sunderland but for me, this is where I want to be.
New boy: Kevin Keen (right) joins Kenny Dalglish, Damien Comolli, Steve Clarke and John Acherberg at pre-season training
'I want to be out training and to help players improve, whether they're 16, 17 or 18 or whether they're 33. I want to get the best out of everyone.'
Liverpool have also appointed Andrew Parkinson to become the club's first operations director from September 5.
Parkinson, currently the general manager for Bluewater, one of Europe's leading retail and leisure destinations, will be responsible for customer services, ticketing, hospitality and stadium operations.
Principal owner John Henry expressed his surprise at how short the summer was for footballers.
'Incredible. A month and a half after the season ends, the first day of LFC 2011/12 training begins,' the Boston Red Sox owner wrote on Twitter.
'MLB (Major League Baseball) has 4 months off. Next stop China (where the club play their first friendly against Guangdong Sunray Cave on July 13).'
The holiday is over, chaps! Premier League stars back in training ahead of new seasonLiverpool add Keen to the Anfield bootroom following the departure of legend LeeTottenham boss Redknapp steals a march on Liverpool for Barca star Bojan All the latest Liverpool news, features and opinion
Explore more:People: Jamie Carragher, Andy Carroll, Kenny Dalglish, Christian Poulsen, Alberto Aquilani, Gianfranco Zola, Daniel Agger, Joe Cole, Martin Kelly, Steven Gerrard Places: Liverpool, Newcastle, China, Italy, Europe Organisations: Boston Red Sox