In-form Coventry are now just six points behind the top six, and Coleman believes they have what it takes to mount a late challenge.
"It's not going to be easy - but it's certainly not impossible," he said.
"The main thing is that the points difference is not insurmountable. Often at this stage of the season, a team comes from nowhere with a good late run - and why not Coventry?
"Two league wins on the trot is a great boost for us, and now we have to keep this run going - starting with Sheffield United on Wednesday night.
"I'm not even thinking about Chelsea in the FA Cup on Saturday yet - we're only focusing on the league match at the moment."
Coventry took the lead on 19 minutes when a cross from ex-Canary David Bell was steered home by Jordan Henderson.
The hosts hit back just after the break when on-loan defender Jonathan Grounds drilled home the third goal of his loan spell, after goalkeeper Keiren Westwood had beaten out a header from Jason Shackell.
The game flowed from end to end after that with chances at both ends, before Fox scored a peach of a winner on 73 minutes - turning his marker Carl Cort inside out before curling a beautiful left-foot shot past David Marshall.
Coleman added: "We have been playing very well of late, with wins over the top two and the FA Cup success against Blackburn, but it was never easy for us against a Norwich side fighting for their lives.
"They made it tough for us, and this time last year we'd have probably lost that game.
"Norwich probably should have had a penalty in the second half for handball - that's how it goes when you are down near the bottom. Fortunately we had that little bit of luck today."
Norwich manager Bryan Gunn did not agreed with Coleman's verdict, after defender Stephen Wright appeared to handle when challenging Cort.
"I should be in here talking about a positive performance and the chances we created," he said.
"But unfortunately I'm concentrating on the referee again, because it has cost us points we would dearly love to have had. The handball with Wright was a stone-wall penalty - but it has not been given.
"It's really frustrating - because having been behind at half-time, I got just the reaction I was looking for. We got a goal back, were on top - and then needed a strong referee to give a decision.
"But unfortunately it didn't go our way. We've had a lot of bad luck recently, and that is another example."
The defeat leaves Norwich in the bottom two, and Gunn is well aware they have a big fight on their hands to preserve their Championship status.
"It's a disappointing defeat, and the other results didn't go for us either," he said.
"But there are still 11 games left and 33 points to play for," he said.