The Blues endured a difficult campaign on the back of winning the title in 2015.
They finished 10th after Jose Mourinho was sacked in December and replaced by Guus Hiddink.
And Costa, who struggled in his second season in the Premier League, admits it can’t get any worse.
Costa, 27, scored 12 Premier League goals in 28 appearances and has called for improvement under Antonio Conte.
He said: “We must not go worse, right? Our campaign last season was really bad. A team like Chelsea can’t do it. We know the importance of our team and we have to be in a better position.
“The coach is working hard. We have noticed that he wants to do things well here and the fans are also hopeful with him. We were needing a change and now it is time to work.”
Chelsea face Liverpool tomorrow at 4am in Pasadena, California at the Rose Bowl.
And Costa insists it will be crucial in their preparation for the new campaign.
He added: “It is a game we want to win and to show the things we are working on in training.
“We have been training hard. Training well before the matches is always important – we know each other and will try to do the things that the coach wants.
“Am I enjoying the trip? Actually not (he joked), because we are training hard (laughing). But it is a beautiful place. We will enjoy if we receive some free time.”