The Reds slipped to their sixth loss in seven games in all competitions at Craven Cottage to leave them nine points off leaders Chelsea.
"It's not even close to being over," said Reina.
"We have to go game by game. Now we must focus on Lyon, which is massive, and after that Birmingham is a must-win game.
"We were a bit unlucky on Saturday. We didn't play as bad as at other times. It was not even close to our worst game.
"It's a tough moment but we have to stick together and try to sort things out on the pitch and in every single training session. We have pride in wearing this shirt and we have to defend it until the end.
"Any defeat hurts someone with ambition and someone who is hungry for titles. But it doesn't matter how many times you fall down - what matters is how many times you get up and keep trying to be the best.
"That's what we have to do now. We have to go back to our principles, sort out the problems we're having and go back to being the Liverpool everyone wants."