Defender Ciaren Jones rose high on the edge of the box to head home in emphatic fashion to give his side the win – with the Hatters defeating Oxford United in the regional final to reach this stage of the competition.
Idiakez was incredibly pleased with his side's performance on the night, as they limited the Latics to few chances.
The former Real Sociedad and Derby County midfielder said: "We have been talking about this for the last four months, the way we played, the way we have been working on the training ground.
"Now today it has paid off, I think we were excellent in the first half and even better in the second half. We created a lot of chances and it was a joy to watch this team at the moment. So you can imagine as a coach how proud I am and it's time to celebrate at the moment!
"We talked about being mentally prepared and I think they are. When you miss a penalty you have to try and create more chances. They did and the way they worked hard to win it back and to keep it, to believe in themselves, it was unbelievable. They showed that to everyone in the stands. Today we have to be proud of everyone at the football club.
"I am really, really proud to be here with this group. At the beginning I was a little bit unsure in the first month. Coming from working with the first team at Derby County. But now from working with them you can see the difference, I am really proud of that."