Nicholls fumbled into his own net under pressure from Jamie Cureton before the same player and Jake Gosling added second-half goals to lift the Grecians above their opponents on goal difference.
"I think we got what we deserved, although the first goal is a foul on Lee," said Boothroyd.
"Jamie Cureton is a wise old fox and he has got his elbow up around him and he has pinned him down. But Lee is 6ft 4in and he knows he needs to come for that.
"I have no complaints about the others - we got done at a corner, we got done at a wide free-kick and a counter-attack.
"You would have to say that we didn't deal with their threat from set-plays which is very unlike us and then we have had three off the line. It wasn't to be our day.
"We have been very difficult to beat but the problem was they scored their goal and it settled their nerves.
"You have to be quite philosophical about it but at the same time we know we need to improve on that because that is not a true reflection on us as individuals and as a team."