The Gulls let in two second-half goals to exit the competition at the first-round stage for the first time since they dropped to non-league in 2014.
"We're a good side when we stick to a game plan," Nicholson told BBC Devon.
"In the first half we executed it and should have been 3-0 up at half-time, but didn't take our chances."
Nicholson continued: "What changes in the second half I don't know. You have to go out and keep doing what you've been successful doing and eventually you'll get your goal.
"I'm disappointed to be out, we were the architects of our own downfall."
The game was Torquay's first without on-loan Forest Green striker Kieffer Moore, who scored five goals in Torquay's previous four league games.
"All the questions are going to be 'is it all about Kieffer Moore?'," added Nicholson.
"It's not. The lads had the chances there, they did the game plan in the first half and they were looking good.
"They have to realise that you cannot go away from doing the basics right. If you do that and you start thinking you're better than what you are, then what's just happened will happen to you."
Torquay United were architects of their own downfall in their 2-0 FA Trophy exit at Braintree Town, according to manager Kevin Nicholson.