Two minutes into the second half, Fulham took the lead on the night, with Ryan Sessegnon smashing the ball home from close range to make it 1-1 on aggregate.
Derby produced a dogged defensive effort to keep Fulham at bay during the first leg and Monday's fixture followed a similar pattern, with the hosts enjoying 67 per cent of possession and managing 10 shots on target to the visitors' one.
Matěj Vydra almost pulled a goal back for Derby in second-half stoppage time, but he dragged his effort wide of the mark as Fulham held on for the win.
"For some reason tonight, we made lots and lots of wrong decisions, " he told Sky Sports.
"If we look at the season as a whole, in some ways, numerous things that have disappointed us in the season have just cost us tonight. When we had the chance to pass the ball, we looked edgy and we didn't handle the ball well enough".
"I said to the players before the game and I said at half-time that we had to attack with more quality and composure, because you could see that we kept giving the ball back to Fulham".
"A draw will take us through, but I don't think that you can play for a draw".
"They were two very, very poor goals for us to give away".
The London outfit will now face the victor of the other semi-final second-leg clash between Middlesbrough and Aston Villa, the latter of which holds a 1-0 advantage.
Derby have become accustomed to life in the second tier since dropping out of the Premier League in 2008 and the failure to progress to the showpiece final at Wembley on May 26 means the Rams have succeeded in just one of their seven play-off campaigns.
He added: "I've been here before in different ways".
"Ultimately, our decision-making cost us tonight".
"It's disgusting at the moment and it's not nice to lose that type of game particularly being 1-0 up, but it's like anything".