But despite the three points there is still a question mark hanging over the future of boss Roy Hodgson, but Cole was quick to point out that there are no doubters in the Reds dressing room.
The former Chelsea star insists the squad are doing their best to ease the pressure on their beleaguered manager.
"We are all behind the manager. We all want to put this club in the right direction and keep working hard," he said.
"We are out there playing for the shirt and the manager. We have all got to stick together because there is no-one bigger than the club.
"I am really happy for everyone at the club; it has been a tough week for everyone - particularly the manager - but we've got the win.
"It is not just the newspapers, none of us like losing and getting criticised but half the battle of modern day football is dealing with pressure and kicking on.
"We are pleased for the fans, the owners and the manager but we have all got to stick together and kick on from here, it can't be a false dawn."
It was the England international's first league goal since his summer free transfer from Chelsea.
"It has been a long time coming and has been stop-start with injuries and suspension," said Cole.
"I just want to play games now and get in the team.
"You can only get fit and get your confidence by playing football."