Valencia went down 2-0 on Tuesday night at home to Norwegian side Rosenborg in the Champions League in Koeman's first match in charge and the Dutchman has called for an improvement on Saturday.
"We need order both on and off the pitch. We must be together, as a group, as a squad and as a club," he said on Friday.
He said: "We need to look forward. With more confidence, we will be able to fight at the top of the table.
"I want us to be mentally strong and express ourselves, but that is difficult at the moment, especially if the players doubt themselves."
Koeman also revealed he has already spotted some flaws in the team's play and said the players are working hard on the training pitch to improve.
"I have seen things I don't like, I have spoken with the captains and the group about how we need to work and we are looking to put those things right," he said.
The former PSV Eindhoven and Benfica coach hopes the team can improve their indifferent home form, which has now seen them lose five times this season at the Mestalla in league and European competition.
"At home the players want to do well, but there are some tough moments mentally," he said.
"We can talk about that and work on it, but the team needs to show their spirit on the pitch. I hope we can do that."