The Chelsea and England legend enjoyed a winning start on his league debut but the Rams were made to work hard by an inspired Royals side.
Mason Mount made the most of Vito Mannone's error to edge Derby back on level terms following Jon Dadi Bodvarsson's opener and Tom Lawrence scored with a 94th-minute header to clinch all three points.
"It's a start for us but we have to enjoy that moment," Lampard told Sky Sports News. "It was incredible character from the lads because it was a tough game.
"We were poor in the first half and Reading made it hard for us to make passes into our attacking players. We were slow in moving the ball.
"We had to find more urgency and we did that. We got back in it with a slice of luck but we made our own luck."
Derby return to action next Saturday with a home game against Leeds United.