City currently lie 11th - two points shy of the play-offs - but have been unable to build any sort of form to challenge the top of the division.
The Sky Blues were beaten 3-2 by Preston at the weekend and Morrison, the club's top scorer this season with five goals, believes his side can gain promotion - but only if they perform consistently.
He told the Coventry Telegraph: "We can't keep doing well for two games and then slipping up because otherwise we will just be up and down the league.
"You have got to be nailed on, week in week out or we will just stay in this league being a top 10 or 11 side which we don't want to do because we want to go to that big league where the best football is.
"When we have got our best team out I still believe we are a match for anyone in this division but we just let our standards slip sometimes and get too complacent thinking we are going to go up the table now."
Morrison, meanwhile, is enjoying having made his best ever start to a season.
The Republic of Ireland international has bagged five goals in eight games with the Sky Blues lying two points adrift of the Championship play-off places.
"I knew what I could do at Coventry," Morrison told the Coventry Telegraph. "I know I started off slowly last season but I knew that with a good pre-season this year and getting the confidence back in myself that the goals would start coming, and hopefully I can kick on from here."