Warriors lost Saturday's semi-final to Connacht 16-11.
Fijian trio Leone Nakarawa, Taqele Naiyaravoro and Jerry Yanuyanutawa as well as Duncan Weir and Tyrone Holmes will all be moving on.
"We've got a great squad and there's plenty of boys more than capable of stepping up already," said Horne.
Brothers Glenn and Kevin Bryce are also leaving Glasgow, but former All Blacks hooker Corey Flynn and Italy wing Leonardo Sarto have agreed to join the Warriors.
"There's a few boys going to leave big gaps to fill," said Horne.
Scotland's Horne bemoaned a lack of discipline as Glasgow lost in Galway and missed out on a third successive final, with this year's showpiece at Murrayfield.
"We were on the wrong side of the referee and we just lost our rhythm," said Horne.
"We didn't get into our shape at all until the first 10 minutes in the second half. When we did we looked really dangerous. We scored a try and we could've walked in another couple if we had moved the ball quicker but ultimately we just committed silly mistakes.
"Everyone in that room, there's another 10 or 20% we could've brought out and we need to make sure that we're more clinical. We've got plenty to work on. That will inspire us for next season.
"In the dark times we'll make sure we think about this and we'll come back a lot better.
"We should've won that game and by a lot of points to spare. It's a real shame but that's rugby.
"They defended well in patches, made a mess of our set piece and when they had the ball in that first half did really well to keep a hold of it.
"We're all absolutely distraught. We threw everything at them but it wasn't our day."
Glasgow Warriors centre Peter Horne is confident the deposed Pro12 champions can recover from the loss of key players before next season.