Lingard joined the Blues on a one-month deal ahead of their clash with Sheffield Wednesday.
The Manchester United youngster scored four goals in City's 4-1 win over Wednesday.
He said: "It's a dream come true. To get four goals and three points on my debut is massive.
"I had a lot of pressure on my shoulders but as soon as the first goal went in I got more confident.
"You can't beat first-team football, so hopefully they will let me stay for the season."
Birmingham assistant manager Terry McDermott said: "Jesse was absolutely unbelievable.
"It disappointed me that he had to come off because I think he could have scored five.
"Hopefully we will get to keep him."