Roberts, who played in goal for non-league Rushden and Diamonds, was found dead at his home on Tuesday.
"I'm absolutely devastated about Dale's passing. He was a really good friend," Johnson told www.mcfc.co.uk. "I grew up with Dale. We were in the same class at school and also played at Middlesbrough together. His parents are friends with my parents and we often went on holiday together."
He added: "I know he was so desperate to improve and get up the leagues, he was a really good keeper, too. My heart goes out to his family and friends and I will really miss him."
Johnson, who is due to play for City tonight against Juventus in the Europa League, added: "I am going to play in honour of Dale and dedicate my performance and hopefully a victory to his memory."
On Wednesday night Roberts' fiancee and parents issued statements speaking of their devastation.
His fiancee, Lindsey Cowan, described the 24-year-old as "my childhood sweetheart and the love of my life".
Roberts, whose death is not being treated as suspicious by Northamptonshire Police, was found dead at his home in Higham Ferrers, near Rushden.