Villa, who have flirted with the unthinkable for the last three years, are approaching crisis point after defeat to Leicester City.
Cole acknowledged: "These are difficult times, we have to accept the criticism that's been coming our way and we need to better.
"This is no time for pointing fingers because we are all going through the same results and frustrations.
"The worst thing you can do is to start blaming each other or looking for scapegoats because this is not one man's problem - it's for all of us to solve together: manager, players, staff and supporters."
Cole added: "I'm very confident in this team, the manager and the collective strength of Aston Villa.
"This is a good club, quite a few of these lads have been in this situation for the last three or four years, they know what it takes to stay up and I honestly think we'll be OK."