Gills striker Cody McDonald netted from close range after Nicholls misjudged a Matt Fish long ball to put the hosts ahead in the fourth minute before Myles Weston smashed in off the post to secure the win in the League Two clash at Priestfield.
Boothroyd said: "It swirled around all night and we paid the price with a mistake from the very reliable Lee.
"I think he is probably the best goalkeeper in the league along with Matt Duke.
"He has been outstanding for us and I am sure he will continue to be. Gillingham are top of the league but I honestly think we were the better side for the majority of the game.
"Myles Weston was in Ben Tozer's pocket for most of the game but he scores and the scoreline looks much more comfortable than it was.
"Gillingham are top of the league for a reason because they get results but if we perform like we did in the first half then we won't be too far away."