Striker John Baird grabbed a dramatic winner just three minutes from the end of extra time at Easter Road to end Rangers' hopes of a domestic treble.
But, with a double still on, Daly is looking for the League One champions to bounce back against his former side Dundee United in Saturday's Scottish Cup semi-final at Ibrox.
Speaking to the club's official website he said: "It's obviously bitterly disappointing. All the boys are gutted and it's frustrating to stand there watching Raith lift the cup.
"It's a hard thing to take. We had great support and we've let both the fans and ourselves down. We had good chances in the game which passed us by and the keeper made one or two good saves as well.
"We will try to use this disappointment next week to go and try to get a win in the semi-final of the Scottish Cup. It's up to us to bounce back from what happened here and we can't afford to dwell on the defeat.
"It will take a few days to get over losing but we have to react the right way and try to use the pain of this defeat against Dundee United."
Watch Rangers take on Dundee United live from Ibrox this Saturday from 12.30pm on Sky Sports 2