The actor, who played the villainous Paul Robinson, said it was “a melancholy day” as he recalled experiences from the past 37 years, including run-ins with the British Royal Family.
The show first aired in 1985 and follows the lives of those living and working in the fictional Melbourne suburb of Erinsborough, with Dennis as one of the original cast members.
Friday marked the final day of filming on the globally-recognised soap, with the final episode due to be broadcast on August 1.
Speaking on the Australian breakfast programme Studio 10, Dennis said he had had to keep a “very low profile” in order to avoid becoming “an absolute mess”.
“It’s a melancholy day for me,” he said.
“I sort of closed the studio door behind me on my very last scene, my very last dialogue scene and... I suddenly surprised myself by getting incredibly emotional.
“I just kept to myself and went to my dressing room... so I’m keeping a very low profile today. I think I’ll just be an absolute mess if I sort of hang around too long.”
Dennis revealed that Diana, Princess of Wales and the Queen Mother had both been big fans of Neighbours and would specifically request tapes from the BBC in order to catch up on episodes missed during royal engagements.
He recalled that the Queen Mother had once snubbed the entire cast of the US sitcom Golden Girls at a meet and greet to talk to the Neighbours cast.
Dennis said he had received a standing ovation from thousands of people at Wembley Stadium at a Michael Jackson concert in 1992, where he had been invited to the VIP box alongside the Prince of Wales.
Fellow cast members paid tribute to the show in a specially curated video where they expressed gratitude for being an “iconic part of Australian culture”.
The final episode will see fan favourites from throughout the years return to the cul-de-sac community of Ramsay Street to bid the soap farewell.
Kylie Minogue and Jason Donovan, who starred as power couple Charlene Mitchell and Scott Robinson in the 80s, were previously announced as returning to the show.
Joining them will be Peter O’Brien who appeared in the show’s first episode as Shane Ramsay, as well as Ian Smith who played Harold Bishop, Mark Little who played Joe Mangel and Paul Keane who played Des Clarke.
Among those returning from the 00s era are Chris Milligan who played Kyle Canning, Morgan Baker as Callum Rebecchi, Natalie Bassingthwaighte who played Izzy Hoyland and James Mason as Chris Pappas.
Pippa Black who played Elle Robinson and her on-screen brother Jordan Patrick Smith who played Andrew Robinson will also return.
Olympia Valance who starred as Paige Smith in the latest era of the show will also return, alongside Jodi Anasta as Elly Conway, Zoe Cramond who played Amy Williams and Kate Kendall as Lauren Turner.
Ben Hall as Ned Willis, Olivia Junkeer who played Yashvi Rebecchi and Zima Anderson as Roxy Willis were also announced as returning.
The show is also credited for helping to launch the careers of other Hollywood stars including Margot Robbie, Liam Hemsworth, Guy Pearce and Russell Crowe.