The Merseysiders have been criticised for their handling of the Luis Suarez affair, both before and after the Uruguay international was given an eight-match ban for racially abusing Manchester United's Patrice Evra.
Liverpool also had to deal with allegations a fan had abused Oldham's Tom Adeyemi in last week's FA Cup tie at Anfield and on Wednesday night captain Steven Gerrard became embroiled in a tunnel row with Manchester City manager Roberto Mancini over Glen Johnson's two-footed tackle.
But throughout their recent troubles there have been visible displays of support, from players wearing Suarez T-shirts at Wigan to fans repeatedly singing the absent striker's name, and Dalglish believes they should harness those sentiments for the coming months.
"When there is a bit of adversity at this club they don't half get together and stand shoulder to shoulder and we may need that from now onwards," said the Scot.
"Any step forward we take we will take together and that remains the case. If we stand together we have got a chance of moving forwards."
Having edged closer to a first final for six years - and a return to Wembley after a 16-year absence - with a Carling Cup semi-final first leg win at City, Dalglish believes they have to focus on the positives ahead of the visit of Stoke on Saturday.
"We have played three games (in 2012), two have been at Manchester City and we've won one and lost one and we've won a cup tie 5-1," he added.
"So apart from the 3-0 (league defeat at the Etihad Stadium) I don't think it has been too difficult (a start to the new year) for us."
Liverpool's defensive display against City was not one Dalglish would usually countenance under normal circumstances but, having taken the lead, it was imperative they kept their advantage for the second leg back at Anfield.
And Dalglish said a gritty 1-0 win had its merits.
"If you are going to go there you need to be good because you can't be lucky all the time," said the Scot.
"The fans would have loved us to have stepped forward a bit more often - and so would we - but there was nothing wrong with the performance of the players.
"We have got a small advantage and we will take that into the next game but it is not going to be any easier next time because they are top of the league and a great side with a fantastic squad of players."