Rowett has acknowledged that the Cottagers were the better team on Monday night, but has blamed the defeat on making too many mistakes all over the pitch.
The 44-year-old told Sky Sports News: "For some reason tonight, we made lots and lots of wrong decisions. I've got to hand it to Fulham but at the end of the day, they've outplayed us. It's a second leg and they've more than deserved to go through.
"Our disappointment is that we've got lots of players in there who've played in these types of games before, but yet in some ways, we've looked the more inexperienced team in the way we moved the ball. But that's what these games do, they test you and you've got to show nerves of steel.
"They were two very, very poor goals for us to give away. We didn't make those mistakes in the first leg; we were very defensively concentrated in the first leg. We didn't do the same in the second leg but did but I think our composure let us down tonight."
Either Aston Villa or Middlesbrough will face Fulham in the final later this month.