While the Rams overcame neighbours Batley Bulldogs at last weekend’s Summer Bash in Blackpool, Doncaster slipped to a 14th defeat of the season and 18th straight loss in all competitions at the hands of Hunslet Hawks.
Victory saw the Rams move back into fourth spot in the Kingstone Press Championship with home games against Doncaster and Workington to come in the next fortnight.
Morrison said: “We have got ourselves into fourth spot and we want to try and stay there for as long as we can and our next two games are important.
“We have to show the right mentality to get the job done as we can not afford to drop points at this stage.
“Every time Doncaster lose, they are getting close to a first win and we don’t want that to come this week.
“I’m pretty close to Hally (Dons chief executive Carl Hall) and I know they have been working hard to improve the squad and try turn things around.”
Morrison was also pleased to see his side grind out victory over Batley, adding: “I think three games in a week took its toll and our energy levels were down.
“There were too many errors for my liking but overall I’d take a derby win any day and our online defence was pretty good.”
Dewsbury have a few injury worries ahead of the Doncaster the game and are likely to rotate their squad once more.
Prop Paul Jackson was taken off after just five minutes of last week’s derby with a back spasm and is a major doubt to face Doncaster.
Ryan Fieldhouse suffered swelling to his knee, while a couple of players suffered knocks to the head.