City striker Callum Wilson scored either side of half-time in a game that the hosts dominated to wipe out their 10-point deduction and climb off the bottom of the table on goal difference.
It could have been more in the end, but Pressley was delighted with the attitude of his players following his call for more.
He said: "I have said to the players, although you think you have given your lot in the first six games, you can always give more.
"I said to them, 'can we squeeze a little bit more out of ourselves?' And boy did they do it.
"They took the game to another level, a great performance, against a very good Colchester side with a good manager, who has done a remarkable job there.
"So to dominate the game in the way that we did is great praise for our players.
"I just want us to get what we deserve. Often you can dominate a game for long periods and one moment, one lapse, one set-play can throw all your good work out the window.
"Jordan Clarke, in the last 10 minutes, had three successive headers in his own box and that is the type of aggression and responsibility we need to see these games through."
Coventry striker Leon Clarke hit both the crossbar and post in the opening period before Wilson converted a close-range rebound in the 37th minute.
The pattern continued after the break and Wilson added a second in the 57th minute, rounding the goalkeeper to tap in after a fantastic one-two with Leon Clarke.