The Blues narrowly avoided an embarrassing FA Cup defeat to League One side Brentford on Saturday, as Fernando Torres' late goal salvaged a 2-2 draw at Griffin Park.
And Terry has bemoaned the west London side's lack of fight in that showing, calling for an instant improvement from his team-mates.
Terry told reporters: “We need to liven up a bit and realise the importance to the fans and the club. I was disappointed, because we didn’t fight and they wanted it more than us.
“Fair play to Brentford, they played well. But we need to liven up.
“Champions League football is a must next season. We saw last season, going to the Champions League final, suffering with all the extra games and stuff like that, we ended up finishing sixth in the League.
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"It’s difficult, but we have a squad. The fact is we’re not winning any trophies at the moment.
"It was disappointing not scoring over two legs of the semi-final and being as lacklustre as we were at Brentford."
Chelsea interim boss Rafael Benitez, meanwhile, insisted he is not distracted by a lack of support from the club's fans and claimed he is simply concentrating on his work.
The former Liverpool boss said: "If I talk about what the fans are chanting, we'll talk about it every week.
"I was talking with Frank and John and David Luiz, about football, and they know the way to change things in football is winning. We were winning nine days ago. We have to start doing that again.
"All I can say is what I know: I have had meetings with Michael Emenalo. We were talking about the situation and it's clear for me the priority is the top four and progressing as much as we can in the other competitions.
"I have some experience. I've been in this job for 26 years and know you have good and bad moments. The way to change things is to work harder and longer. That's what I'm doing.
"When I'm asked questions about the club, or the future of players, it's said I'm the 'interim manager'. If I'm the interim, my job is to improve the team and the players on the pitch.
"You have to be judged on results. I have a responsibility, but that responsibility is trying to bring the best from my players. I cannot talk too much about my views on the system and structure of the club. I have to concentrate on my job.
"Of course I know what has happened here in the past, but this is another time - a transitional period. We all know that."