The Blues, who beat Rubin Kazan 3-1 in the Europa League quarter-final first-leg tie at Stamford Bridge on Thursday, also have an FA Cup semi-final against Manchester City on the horizon.
But for Terry, Sunday's visit of struggling Sunderland takes precedence as Chelsea vie with London rivals Arsenal and Tottenham for the Champions League spots.
"We must win and keep winning games in the league and really push," the 32-year-old said.
"Because that is what this club feeds off - the Champions League. We must be involved in that."
Meanwhile, Terry expects Sunderland to be galvanised for their visit to west London following the appointment of Paolo Di Canio as new manager.
"It's going to be really tough," Terry added. "A new manager has come in, a fantastic player he was as well. He's certainly going to have them up for it.
"You could see how well organised Swindon were over the short period of time he was there.
"He'll show passion. I've read a few things: he's told them 'tell your wives and your families it's going to be a lot of long days and hard work'.
"I think that's what they need because they're a great club, they've got a great set-up there and a great set of fans. The players are really good as well.
"It's surprising to see them down there, when we've seen them fight for so many years.
"They'll certainly be fighting and coming here hoping to pick up something."