The outgoing European champions, who qualified for the tournament this season by virtue of their dramatic success over Bayern Munich having finished sixth in the Premier League, are again locked in a battle for a top-four finish.
Their 3-0 victory over Fulham on Wednesday night, in which Terry scored twice after being restored to the starting XI, saw them climb to third in the table as their scrap with Arsenal, Tottenham and Everton promises to go down to the wire.
But with a testing fixture list over their final five matches, Terry knows the importance of remaining ahead of their rivals if they are to replicate last summer's business, when Eden Hazard and Oscar were two of the eye-catching arrivals at Stamford Bridge.
Terry said: "It was nice to start but the most important thing was to win because it was our game in hand on the others going for the top four. It was our first away win for a while and gives us good momentum for the final month of the season.
"We've a really tough run-in with Liverpool, Manchester United, Spurs and Everton still to play.
"But the top four is an absolute must in terms of moving forward and maybe the signings we make this summer."
David Luiz opened the scoring with a glorious long-range effort against Fulham, with the Brazilian backed to inherit the armband from Terry in the future, a decision which has the long-term backing of his fellow centre-back.
Terry added: "I hope to wear the armband for a few years yet. Petr Cech will get the armband next because he's been here the longest.
"But when you look at David Luiz, I think he can be my long-term successor. He's still young, he's still learning, but he'll be a very, very good player.
"He has the personality to push the lads and he's like that in training as well as during games. He demands a lot from himself and everyone around him and that's good for the squad."