Wright became a father for the second time with his partner Sarah on the day after City went out of the FA Cup to Portsmouth.
Speaking to the CT, Wright said: "My fiancée Sarah had a few twinges over Christmas and we thought the baby was going to come at any time, and so I had a car down at Portsmouth for the first FA Cup game just in case.
"I said to her on the Tuesday that if she was going to go into labour it would be best if she could do it in between the Portsmouth and Ipswich games and in the end I went straight home after the Pompey replay at the Ricoh and her waters broke about 1.15 in the morning.
I couldn't sleep anyway and ended up not sleeping for 36 hours and our second son was born at 10.34am on the Wednesday.
"We have called him Thomas Daniel, who weighed in at 8lb 14, so he's a little brother for our four-year-old lad Daniel. We have had to spoil the older one a touch because he has had all the attention all this time and now he is having to share it, so there's a little bit of jealousy. He was born at Solihull and it was amazing.
"The snow came in blizzards while we were in hospital so he was born on a snowy day just the same as Daniel who was born up in Sunderland.
"The timing of the birth helped take my mind off the disappointment of the football and put it all into perspective really.