Brian McDermott's side couldn't find a winner against the Canaries at the Madejski Stadium last time out, but they welcome David Moyes' high-flying Everton on Saturday.
The Toffees put an end to to four successive draws after coming from behind to beat Sunderland 2-1 in their last encounter, but Morrison is predicting a potential upset.
"We're so close. We're literally an inch away from doing the right thing," he told the Reading Post.
"If those draws can turn into wins then we will be fine."
Reading have endured a tough start to life back in the top-flight and they remain stranded in 18th place following a run of 10 games without a win.
They are unbeaten in three Premier League games, but after throwing away a seemingly invincinble four-goal lead against Arsenal to lose 7-5 in the Capital One Cup, the 21-year-old was delighted to finally get that clean sheet.
He added: "It's all about getting clean sheets as a defender. We're really proud of that and I think we deserved it.
"It was a bit of a nothing game [against Norwich] and there weren't many chances at either end. It's another point on the board.
"We have to build on this and go on to the Everton game."