Rowett was furious after his side lost a two-goal lead to be held 2-2 at St Andrew's to end any hope of making the Championship play-offs.
"We've held on to leads at lot better this season," Morrison told BBC WM.
"We're probably far too open - we need to get that bit between our teeth."
Rowett called his side "unprofessional" and "lacking desire" after seeing Clayton Donaldson's brace cancelled out by two goals in the last 17 minutes, with Greg Cunningham's equaliser coming a minute from time.
"We need to see the game out, especially at home - they had no right to get back into it," said 28-year-old Morrison.
"It was very disappointing and a few choice words were said.
"Early on in the season, we had a tighter shape and people were working harder maybe to be more difficult to beat."
Blues went into the game with only a mathematical chance of finishing in the top six but the result has now extinguished their promotion hopes.
"It's a difficult time after such a good season and it turning out the way it has," added Morrison.
"It is an anti-climax, the fans are disappointed we're not still chasing the play-offs and that does affect the players but we're still going to put 100% in."

The 28-year-old was an ever-present in the side which won the County Championship title in 2016.
"He is one of the finest cricketers in the country," managing director of cricket Angus Fraser said.
"As a glove-man there are few better than him and he is capable of producing match-changing innings with the bat."
Since making his debut for Middlesex in June 2009, Simpson has made almost 250 appearances in all formats.
The left-hander has scored 6,687 runs for the club and has 472 dismissals to his name.

Nats Prestwick expects to handle more than 250,000 flights during the peak holiday season this year - an increase of 15,000 on last year.
The company has announced a Â£600m investment in a new computer system.
But it says government support is needed to improve the network of "ageing" flightpaths.
Paul Peers, head of development at Nats Prestwick, said: "We are predicted to have the highest amount of traffic we have ever had for a summer period this year.
"We are expecting to have around 15,000 more flights just in July and August compared to last year.
"We are ready for that and our controllers have been doing a great job up to this point making sure that we minimise the delays that people see and making sure that we keep people safe in the skies.
"We have been preparing for this since November, so the summer doesn't come as a surprise to us, and we have a series of events to make sure our controllers are ready for the summer traffic.
"Indeed, this year, the build-up in traffic has helped us with that because we've had record days already that our controllers have dealt with extremely well.
"But one of the big challenges for us is the design of the airspace in the future and the traffic growth."
He added: "We are investing over Â£600m over the next few years in the technology systems.
"In fact, at the Prestwick centre we are proud to say that we have the first version of iTec, our new flight data processing system, in operation already and that is the first in the UK.
"The skies are getting fuller every year and we are expecting to see increased traffic growth.
"But if you think about the airspace as effectively motorways in the sky, if you think about 1970s motorways with today's car traffic, we are in a similar scenario.
"We are going to have to redesign our airspace and we are going to need government support to make sure we can do that in the right way."
Captain Michael Morrison says the Birmingham City players have accepted the criticism aimed at them by manager Gary Rowett after their draw with Preston North End.
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Middlesex wicketkeeper-batsman John Simpson has extended his contract, keeping him at Lord's until the end of the 2019 season.
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The national air traffic service (Nats) has said a "massive" programme of modernisation is needed to keep up with demand for air travel.