A wonder goal from Luke Guttridge was enough to seal their place at Wembley against Bradford but Nicholls kept their 1-0 lead from Thursday's first leg intact with a fine save from Marlon Pack's 14th-minute penalty. Nicholls went on to make several outstanding saves over the course of the match, much to Boothroyd's joy.
"I thought he was outstanding," the Northampton boss said. "I was fortunate at my previous club to work with (West Brom goalkeeper) Ben Foster and I genuinely think Lee is as good as he is."
He added: "We are very pleased but you have to feel for your opponents - it's not nice to go out in the semi-finals. Respect to them as they have put us right under the cosh. We didn't do a lot with the ball but we were strong and resolute. I think that our last few away games have seen us play well so I was quietly confident. We played to win the game.
"The triangle of Lee Nicholls, Nathan Cameron and Clarke Carlisle were absolutely brilliant. We have managed to persuade a lot of players to come to our club in League Two who shouldn't really be here and that's a credit to our chairman. There are players here who have played at a higher level and who will play at a higher level.
"I am really thrilled for the club that we are going to Wembley but it is important that we play the game and not the occasion. I don't want to go for a day out, I want to go and win. It is against my club so it will be an emotional one for me. It's where I'm from and where I was brought up so it will be weird."
Cheltenham manager Mark Yates said: "If we would have played all night we still wouldn't have scored but the town can be very proud of its players. Their goal was a great strike and Scott had no chance with it. We were the better team on the night and they were the better team last Thursday and unfortunately things haven't gone for us.
"Marlon is disappointed in the dressing room because he thinks he has let people down - there are tears pouring down his face. But Marlon Pack has been magnificent for the past three seasons at this football club.
"He stood up in front of a packed house and was brave enough to take a penalty. There were plenty of others who wanted it but he did it as he has all season and unfortunately the keeper's guessed the right way.
"The boys have to pick themselves up and have a good night out in Cheltenham. They have been fantastic all season. Our resources don't get near a lot of clubs in this division but that just shows how decent we are."