Liverpool’s 3-0 victory over Everton in the Merseyside derby in March marked the Reds’ only success in their last eight home games, a run which includes shock defeats by Fulham, West Bromich Albion and Wigan Athletic.
Dalglish’s side suffered a 2-1 loss to Chelsea in the FA Cup final on Saturday, and the 61-year-old is desperate for Liverpool to finish their home games on a positive note against the Londoners.
“It would be fitting if we could finish off at home with a victory,” Dalglish said.
“Everyone knows the home results haven’t been great this season despite some excellent performances along the way.
“It would be a little bit of solace for the punters who have given us tremendous support throughout the season if we could get a win.
“We want them to go home with a certain amount of satisfaction and we can do that by getting the three points.
“It would be fantastic for everyone to get a positive result – for both the players and the supporters.”
Ramires and Didier Drogba scored either side of half-time in the Wembley showpiece before Andy Carroll halved Chelsea’s lead – but the Blues held firm to win their fourth FA Cup in six seasons.
And Dalglish hinted that he will field a full strength side for the visit of Roberto Di Matteo’s Champions League finalists.
“We will need to assess how everyone is after the weekend,” Dalglish added.
“We will see what we’ve got as a few bumps and bruises may well have cleared by Tuesday morning.
“We’re not going to give anything away but it will be the strongest team we’ve got from the players available.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news