The Irish winger scored twice as the Hibees came from behind to beat Hearts 2-1 and leapfrog their Capital rivals into fifth spot in the table.
Former Dundalk and Preston man Horgan said: “This is right up there in my career. The whole day was special.
“The atmosphere from both sets of fans was incredible, real hair standing up on the back of your neck kind of stuff.
“It was an incredible feeling. We haven’t won here in six years, so to come from behind, get three points and jump ahead of Hearts all in one – it’s fantastic.
“At the end of the day, it’s three points and we’ve got five massive games coming up now. We want to get as high up the table as we possibly can.
“Thankfully we won the game, so all’s good at the minute.”
Hibs were 11 points behind Hearts when Paul Heckingbottom was appointed manager in February. Now Horgan admits the Easter Road side have ambitions of catching Aberdeen and Kilmarnock in the race for Europe.
Heckingbottom’s men begin their post-split fixtures with a home match against Celtic on Sunday, April 21 and Horgan said: “The run we’ve been on since the gaffer came in has been just unbelievable.
“We were eighth, five points behind Motherwell, and the target was sixth at that point.
“But we’ve gone on a brilliant run of form, we’re unbeaten in eight games and we’re playing some good stuff.
“We want to finish above everyone, not just Hearts. We want to get as high as we possibly can. If we can finish third or fourth, that would be fantastic.
“We want to drag Kilmarnock and Aberdeen back into us. That will be the aim for the next five games.
“Every game is going to be a scrap and a fight, but if we play like we did on Saturday, there’s no reason why we can’t do that.
“I’ve played in Europe before. It’s special to be involved and they’re great nights. So we have some huge games coming up.”