It has also been widely reported that the jobs of GM Scott Howson and head coach Scott Arniel could be on shaky grounds.
"Obviously, I'm disappointed with the start," Priest told the Dispatch. "I'm very frustrated by everything the team has had to endure that's been somewhat outside the norm of what you'd expect.
"The (James) Wisniewski suspension. The injuries to players who make an impact, in their own way. You have to overcome those issues, but at the same time it still seems like all of the excitement felt by the fan base has ... we've kind of let the air out of the balloon."
The Blue Jackets boast the fifth-highest payroll in the NHL, but will receive plenty of cap relief due to long-term injuries to forwards Kristian Huselius, Jared Boll and potentially Jeff Carter, who is now out indefinitely with a broken foot.
Priest wants to see how the team performs as a full unit before he begins to judge the performances of Howson and Arniel.
"I absolutely feel (that we can win)," he said. "Time will tell, but we are absolutely committed to winning. We demonstrated that this summer, and we're not going to rest until we win. We hoped we wouldn't be where we are. We have to keep pushing through this, but we also need to see our team. We don't have our team.
"When we have our whole team assembled, and we have time to digest it, then we'll be able to really take a hard look and evaluate it."
Howson admits to receiving trade inquiries, as teams have called about the likes of forwards Derick Brassard, Antoine Vermette and Samuel Pahlsson, and defenseman Marc Methot, but nothing is close to happening.
However, Howson warned "you can't sit idly by and let this continue on this course."