Royals led United twice before slipping to a rollercoaster 4-3 defeat at Madejski Stadium last weekend.
It was their third league loss in a row, leaving Brian McDermott's men 19th in the table and four points from safety with a game in hand.
But Morrison believes they can take plenty of confidence from their display against the Reds heading into a critical week, with Reading facing back-to-back away fixtures at fellow strugglers Southampton on Saturday and then Sunderland next Tuesday night (7.45pm ko).
Southampton currently lie 18th, three points ahead of Reading, while Sunderland are 17th with one point more.
And centre-back Morrison, who was on the scoresheet against Sir Alex Ferguson's star-studded outfit, stated: "Saturday is a massive game and some people may call it a six-pointer. We're amongst a group of teams down near the bottom and now we need to go to Southampton and pick up three points.
"It doesn't matter how we do it but that has to be our goal now."
He also insisted: "If you look at Manchester United's goals, they were all fairly soft apart from maybe Robin Van Persie's fourth one. It's not like we were ripped apart.
"It was disappointing but all we can do is take the positives from that into Southampton."
Saturday's loss against United equalled a Premier League record with all seven goals coming in a madcap 26 minute period.
But Reading were the masters of their own downfall having gifted the visitors at least half their goals.
Hal Robson-Kanu fired Reading ahead, Anderson equalised then Wayne Rooney gave United a 2-1 lead from the spot.
Identical headed goals from Adam Le Fondre and Morrison himself in a three-minute burst saw Royals edge 3-2 in front.
Sadly, they couldn't hold on as Rooney made it 3-3 and Robin Van Persie added a fourth moments later.
In truth, Royals keeper Adam Federici was at fault for Anderson's leveller and Jay Tabb gave away a needless penalty when he bundled over Jonny Evans with Reading 2-1 in front.
Morrison, who is attracting interest from Arsenal, admitted: "It was a bit mad. The first-half was one of the craziest 45 minutes of football I've ever played in.
"The first goal went in at the front post and the second was a penalty.
"We felt comfortable in our shape and in the second half they sat there and made it hard for us to break them down.
"I think we can take away a lot as they're one of the best teams in the world.
"But I would exchange that goal for a point or three any day of the week."
l READING FC are set to lock horns with legendary boss Steve Coppell in the FA Cup third round.
Royals have been draw away to League One Crawley Town where Coppell is now director of football.
The cup tie will take place at Broadfield Stadim on the weekend of January 5/6.