Kenny Dalglish has warned his out-of-favour Liverpool players that he will not be afraid to buy replacements if their attitude to being dropped alters.

Dalglish began last Sunday's 2-1 victory at Chelsea with three of his biggest signings – Andy Carroll, Stewart Downing and Jordan Henderson – on the bench. Collectively, the trio, who each featured at some point at Stamford Bridge, cost around £75m and, although the Liverpool manager said he was delighted with the spirit they have demonstrated, he added it would be "their problem" if they were to show any inclination to sulk.

"At the end of the day it is hard for those who don't play," he said. "It is hard to keep them motivated and keep them going. That is understandable. If they come in with really good attitudes and not with petty lips when they are left out, it is helpful to everyone.

"For them to have come in with positive attitudes has shown their determination. It hasn't done anyone any harm. If they are not committed to playing, it is not going to be my problem, it is going to be their problem because we will go and get people who are determined to play."

To illustrate his argument that his Liverpool side are entirely united, Dalglish pointed to a photograph that showed Downing celebrating after Liverpool's last-minute winner at Stamford Bridge. "Did you see Stewart Downing's face when Glen Johnson scored?" he asked. "Print that picture rather than use any words from me to describe how he felt. It says more than I could ever say."

Of the five major signings Dalglish has made, two – Luis Suárez and Charlie Adam – appear at this early stage to be unequivocal successes. Henderson has had his moments while Downing has faded after a bright start. Concern over Carroll, evident at the start of the season, has simply deepened. The former Newcastle United striker, signed for £35m in January, has managed only two goals this term and is the subject Dalglish is most often asked about. On Thursday he said that, despite the fact that Carroll had scored twice against Sunday's opponents, Manchester City, last season, he was not guaranteed his starting place at Anfield .

"You take into account what is happening now," Dalglish said. "Just because he scored twice last season doesn't mean he's going to score this time. We will all start afresh, Andy included. For the record I thought Andy's best two performances were against Stoke and West Brom."

Neither of these matches was at Anfield and nor were they against teams of Manchester City's sophistication. That 3-0 win over Roberto Mancini's side in April would probably count as the high-water mark of Dalglish' s return and featured a clean sheet and a fine performance from Jamie Carragher.

Liverpool have kept one clean sheet in their last six games at Anfield and that was not enough to earn a win over Swansea, while some have seen Carragher's omission at Chelsea as a sign that a great career is drawing to a natural close. "You do whatever is necessary for the team," said Dalglish.

"If we hadn't won at Chelsea, it would have been a bad side. We don't have hindsight to work with. Carra has only been back a week after his calf injury but you know what he has done for this football club. He understands."

Dalglish has ruled Steven Gerrard, who has not played since 22 October because of an ankle infection, out of Sunday's visit of City. "Like we've already said, we are delighted with the progress he's making and we've said that we won't put a date on his return – and we won't put a date on it now," he said of the captain.