Substitute Leam Richardson smashed home a last-minute volley to give the Lancashire club a 2-1 victory that keeps them on the coattails of the top seven teams.
"I think it was a hard-fought game. Cheltenham are a handful and put us under pressure, especially in the second half, and we had to be at our best," said Coleman. "I thought we dug in and it was a magnificent performance. The move for the first goal was fantastic and the finish for the second was fantastic.
"It's a good win but they've got to back it up on Tuesday against Shrewsbury. If we apply ourselves we can match ourselves against anyone in the league. Cheltenham will be up there at the end of the season and why can't we?"
Coleman reserved special praise for match-winner Richardson and added: "He's a very good professional, he's a credit and great ambassador for the club and great role model.
"He was blighted by a terrible injury that might have finished lesser characters off but he's worked his socks off and soldiered on through a lot of pain and frustration and is a valuable member of the squad."