Second half goals from Ryan Sessegnon and Denis Odoi earned Fulham the victory as they seek a return to the Premier League which they were relegated from in 2014.
Rowett was reluctant to criticise his players, but he admitted that he wanted to see more from his team on the night, especially in the final third.
"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". We didn't make those mistakes in the first leg; we were very defensively concentrated in the first leg.
Fulham attacked from the outset but Derby keeper Scott Carson frustrated them throughout the first half with a series of fine saves.
Fulham goalkeeper Marcus Bettinelli, beaten by Jerome's strike in the 34th minute, believes his side will overcome the one-goal deficit and progress to the final.
He said: "Fulham are a good side, we know that. We've got nothing to lose, we're great going forward, so we're in a positive frame of mind going back to the Cottage".
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"They are two poor goals".
"They outplayed us in the second-leg and they more than deserve to go through".
The teen is often centre of attention but said: 'I just try to play my own game.
"Ultimately, if you do that, then you have to hope for the flawless defensive performance and I don't think that you can expect that twice with such a short turnaround".
'I just get my head down and work hard for the team'. But that's what these games do, they test you and you've got to show nerves of steel.
But for us, we've got to use that disappointment to look at things we need to do better.