He added: "There's a lot of young players at the club, we've got that respect already and it's something that I think everyone around the club and the supporters is really going to enjoy."
Thompson stepped into the breach to take charge for Tuesday's defeat to Bristol Rovers, but the club have moved quickly to find a permanent boss.
Skiverton, who has taken his Level Three coaching assessment and is set to sit for his A Licence in the summer, admitted to having to think long and hard about taking the position.
And after taking advice from former Yeovil boss Gary Johnson he decided the time was right to step into management.
"I'm putting my reputation and everything I've done for the club in the past a little bit on the line, but the opportunity was too good to turn down," he added.
"It's something that excites me and it's going to be an exciting time.
"The club's moving in a different direction now and it's a chance for a young British team to have a crack at management and that's something that I've been heading towards.
"The opportunity has come quite early for me, but it's something I'm willing to take on."
Former boss Johnson backs Skiverton
Johnson, who was at the Yeovil helm from for four years and led them into the Football League with Skiverton as his captain, described it as a "great" appointment.
"He's had opportunities to move on, but he's stayed there and he deserves a crack at it," the Bristol City boss told BBC Points West.
"It's not easy to turn from a player to a manager sometimes, especially when you're one of the lads, but he will do.
"He knows the game and has got some influential people who will help him if he needs it. I wish him well and I think it's a clever appointment."
Chairman John Fry, who refused to elaborate on the sudden departure of Slade, denied the charge that appointing an inexperienced manager was the "cheap option".
"It couldn't be a better appointment in my view," he told BBC Points West.
"We are ambitious, the changes have been forced on us and the persons concerned are ambitious.
"I think we've made the right appointment and it shows we are the sort of club that will invest in people like Terry Skiverton and move it forward."
Fry rubbishes 'cheap option' barb
Yeovil climbed clear of the relegation zone with four successive wins in Slade's final games at the club, and Skiverton says his initial priority is to maintain that momentum and stave off the threat of relegation.
"Oldham on Saturday's a big game and I'm hoping the support will come out for me, which I think they will do," he said.
"We've been on a great run recently, we had little bit of a blip against Bristol Rovers, but the boys are in a confident and spirited mood.
"The thing we've got to do now is kick on, get some good performances in and do a lot of work on the training pitch.
"It's not going to come overnight. We need to work really hard and then we'll start to see things come to fruition.
"That's the thing that I'm going to take most enjoyment from, seeing the work that we do on the training pitches come on to the pitch and I think we're going to surprise a few people."
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