After going a goal down in the first half, the Hatters replied in the second 45 minutes through Josh Neufville, before going onto win 4-2 on spot-kicks.The Town's opposition in the final is still to be decided with Exeter City taking on Oxford United in the coming weeks.
Idiakez said: "It was really good. First half we started quite poorly – the first ten minutes we weren't at it. After that we were excellent.
"We created 23 chances, some of those were one-on-ones, but it was one of those games where you are in control and you don't think you're going to score. It's impossible for me to be happier. It was a joy to watch. I have said before that since the Youth Cup defeat to Stevenage, the attitude has been incredible."
After the sluggish start against the Robins, the Hatters took control of the game and the former Derby County midfielder was exceptionally pleased with his side's focus as they went in search of a way back into the game.
"Cheltenham scored after we started poorly, but the reaction was immense," Idiakez continued. "When you're losing sometimes teams play the long ball or lose discipline, but we didn't – we were focused and it paid off.
"For our goal we played out from the back, created a two-against-one before Josh Neufville tucked it away to level the score. We thought it was going to be one of those days, but our hard work and perseverance paid off."
Idiakez was known for being a set-piece specialist and a deadly penalty taker during his playing career – something he hopes rubbed off on the players when they put in an extra shoot-out session in training on Friday.
He said: "We practiced penalties on Friday and it worked. You never know with penalties. I took penalties as a player, and we went through it, and it went our away.
"We don't usually practice penalties, but we did because it was a cup competition so we knew it was a possibility, so I was delighted to see us put away all of ours."
The Hatters head to Northampton Town tomorrow as they look to climb the league table, with Idiakez wanting to see the same effort levels put in against the Cobblers as he saw in the Cheltenham game.
"We want to finish in the top six," he added. "We are currently tenth, and if we win then we can go into the top six. We want to finish the season well. We want to focus on the league and finish as strong as possible, I don't want anyone to relax. The second years are hoping to get pro contracts, whilst the first years are really pushing on."
If your want to see the youth team in action at Northampton Town, kick-off is at 1pm at Moulton College, NN3 7QL.