Kenny Shiels' side's 2-0 victory ended a 57-year winless hoodoo at Parkhead, and while Pascali revelled in the celebrations, he urged his colleagues to show the same application for the rest of the campaign.
Kilmarnock are home to Inverness in the league this Saturday and Pascali wants the Celtic victory to be the springboard for a sustained run of form.
"It was fantastic and it was important for us to enjoy every minute of it," he said. "This is something so rare and you need to take it all in.
"For me, it was great because when Kilmarnock won the League Cup last season at Hampden I was injured and you never really feel as though you are part of it.
"So to be able to be part of a victory that has taken so long to come is a great feeling.
"We did celebrate a lot in the dressing room because it is a big thing for us. But I've been involved in good performances one day and then fallen in the next game.
"So although I want us to celebrate and remember the feeling of beating Celtic, I also think we need to show the same spirit and togetherness this weekend when we play Inverness.
"That game is every bit as important as this one was and we want to start pushing ourselves on."
A first-half goal from former Hoops kid Cillian Sheridan and a second-half penalty from Liam Kelly gave Killie victory. Pascali was particularly delighted for Kelly.
The midfielder's father died suddenly at Hampden last March when Kilmarnock won the League Cup so the celebrations that day were understandably muted.
"I was thrilled for Liam," said Pascali. "We all were. It was emotional for him. It was a big thing for him to keep his concentration and score the penalty, but I thought he took it very well.
"For him and his family it is a happy thing for them to be able to celebrate and enjoy."
Pascali also felt his side were able to exploit the flatness about the stadium on Saturday afternoon. While Celtic appeared lethargic and slow, there was no edge on the terraces either.
Much of that can be attributed to the lack of the Rangers breathing down the necks of Celtic this season and therefore no genuine tension in matches, but it is something that has not gone unnoticed by opposing teams.
"I was surprised at how quiet the Celtic fans were," said Pascali. "In my time in Scotland, that's the quietest I've heard it.
"Celtic had a great game in Barelona last week and it felt as though everyone was very drained after it, including the supporters."