Didier Drogba opened the scoring when he fired his seventh goal at the new Wembley to give Chelsea the advantage, before Juan Mata was dubiously awarded the Blues' second.
The ball did not appear to cross the line but referee Martin Atkinson blew his whistle and awarded the goal, much to the fury of the Tottenham players and supporters.
Spurs winger Gareth Bale then pulled one back for Harry Redknapp's side, but Ramires' 77th-minute strike gave Chelsea an unassailable lead.
Frank Lampard added the fourth from a powerful free-kick with Florent Malouda sealing the win with an injury-time strike.
Terry was in the goalmouth scramble when Mata's strike did not appear to cross the line and believes goal-line technology should be brought in.
"I thought it hit me and stayed out but I haven't seen it on the replays," Terry told ITV.
"We've been calling for goal-line technology for a very long time.
"Let's hope that people make the right decisions.
"It was an important game today [Sunday] and fortunately it went our way. Throughout the season things go with you and go against you and today [Sunday] it's gone with us and we're delighted.
"I thought we were the better side and scored some great goals."
Tottenham captain Ledley King called into question Atkinson's decision to award the controversial goal.
"Obviously I haven't seen it again but from where I was I didn't think it crossed the line," King said.
"The referee said he made the decision and I find it hard to believe he could see it from where he was.
"There's nothing you can do. He makes the decision and it's a massive decision at the end of the day.
"You expect the linesman to have made it. At 2-0 down you know it's going to be a tough game against Chelsea.
"We got ourselves back in the game at 2-1 and we've just been caught out trying to get that second goal and we've been picked off."
Lampard, who went on to score himself, claimed not to have seen the second goal as he took the corner, but believes Chelsea deserved the victory regardless of whether it should have been awarded.
"I didn't see it," the midfielder said.
"Fair enough if we got lucky there, we got lucky. The referee's given it.
"We didn't have a conversation about it. We scored a lot of goals and created a lot of chances today [Sunday] and over the course of the game we deserved to win.
"It was an amazing game. I thought we played brilliantly. The first half was tough.
"Didier scored an absolute belter. I think we deserved to win that game with the amount we created. Tottenham are a top side but today [Sunday] we won it well."