Dunne admitted he was considering his future after Saturday's 2-1 home reverse at the hands of fellow strugglers Scunthorpe - a ninth successive league defeat and an unwanted new club record - left the U's in League One's relegation zone.
But Cowling has revealed it did not take him long to convince Dunne he remained the right man for the job, and has also cleared the addition of as many as three new signings this week.
The U's chief told Colchester's official website: "Joe has been at Colchester United for a long time, cares passionately for the club, and only wants what is best for it.
"Therefore, following a run of defeats it was only natural for him to consider alternate solutions, including his own job.
"However, I still have every confidence in Joe's ability to turn the situation around and when we spoke after the game, it wasn't long before our conversation turned around to how we move forward and lift Colchester United out of the bottom four.
"Fans can expect two or three new signings this week before we go to Hartlepool on Saturday with even more determination to reward our loyal fans for their support and to get winning again."
Chelsea goalkeeper Sam Walker has already been brought in on loan until the end of the season, while former loan striker Jabo Ibehre also appears set to return to the Weston Homes Community Stadium this week.