Morais said: “I am delighted with the win, the performance and attitude of my players.
“I am expecting many surprises from my players as I am a positive person. I believe in their quality, I believe in them and I believe that they can do so much more.
“I do not think about relegation. There are a lot of games to be played and we will win enough games.
“This result was important and the win over Birmingham is a big motive to celebrate.”
Barnsley recorded only their second win in 18 games at St Andrew’s.
They bounced back from their 4-1 defeat against Millwall and their success was carved out by Oli McBurnie, who is on loan from Swansea.
He opened the scoring after 12 minutes, then missed a penalty only to be on hand to notch his second goal in the 36th minute.
Beaten Birmingham dropped back into the relegation area as they slumped to their fourth successive defeat with their fans calling for the head of manager Steve Cotterill.
Birmingham’s first direct attack produced a commendable double save by Barnsley goalkeeper Nick Townsend.
The two saves were followed by the Tykes storming into a 12th-minute lead.
A cross from Mamadou Thiam was met by McBurnie who hooked the ball into the net to the right of David Stockdale.
Matters could have become even worse for the hosts in the 16th minute when Marc Roberts impeded McBurnie.
However, McBurnie then wasted the penalty as Stockdale dived low to his left to make an excellent save.
Barnsley, growing in confidence against a disjointed Birmingham, applied a killer touch when McBurnie was again on the mark in the 36th minute.
Stockdale saved a close-range effort, but was unable to maintain possession, which allowed the alert McBurnie to turn and fire home from a couple of yards.
The Tykes resolutely defended their lead as Birmingham attempted to atone.
Birmingham City: Stockdale, Jenkinson (Bramall 83), Roberts, Dean, Colin, N’Doye (Jota 66), Gardner, Boga, Maghoma, Adams, Gallagher. Unused substitutes: Jutkiewicz, Lowe, Dacres-Cogley, Morrison, Trueman.
Barnsley: Townsend, Yiadom, Jackson, Lindsay, Fryers, Potts, Joe Williams, Gardner (Pearson 87), Thiam (Mahoney 60), Moore, McBurnie (Knasmullner 77). Unused substitutes: Davies, Bradshaw, Moncur, Cavare.
Referee: J Simpson (Lancashire).