Terry’s goal on the stroke of half-time put Chelsea in front at Wembley and a Diego Costa shot that deflected in off Kyle Walker 11 minutes into the second half secured a 2-0 win.
The trophy is the first Chelsea have won since Jose Mourinho returned to the club in 2013 but Terry hopes it is the first of many for the current crop.
“That’s the first trophy, it’s massive,” Terry told Sky Sports. “It meant an awful lot to us (to win the League Cup) in 2004-05 in Jose’s first year here.
“That (Sunday’s win) could be the start of something very good but we have to kick on and we have the league to focus on, but it’s a great day and a great win today.
“The pressure was there before the game, obviously, but that’s what cup finals do to you. I thought we played very well, handled the game very well and (we are) delighted with the win.
“I think it was fairly even first half, second half I thought we controlled it a little bit better and (were) deserved winners.”
Cesc Fabregas and Diego Costa also gave their reaction to the victory, with Fabregas full of praise for his Spain team-mate.
“In games like this you need your best players to perform, and he (Costa) did it today,” Fabregas added. “That is why Mourinho loves him, and why Roman Abramovich made the effort to sign him in the summer.”
And Costa insisted that despite the second goal taking a huge deflection off Walker, the goal is his.
“Of course it is mine, who else? If I don’t shoot I don’t score,” Costa said.