Rudden signed on loan from Rangers with time ticking away on Friday's deadline, but manager McKinnon was keen on Celtic youngster Tony Ralston too.
"We tried to bring in Ralston from Celtic as well. We were trying to do a couple of things late at night. We were close, but we got Rudden that was brilliant.
"It was so late, we were trying to settle with players at 10 at night. It was mad."
Along with Ralston, the 48-year-old, who was officially announced at 9.50pm on the club's Twitter channel, had Darren O'Dea offered to him on deadline day.
"We had Darren O'Dea getting punted to us at 10:30 at night by Neil McCann. I was in the house!"
McKinnon, though, was delighted by the signing of Rudden, who was training this week and is in contention to play this weekend against Ayr United.
"Zak is only 18 but the reason we have been chasing him is because he works hard, he's got great legs and he scores goals. We are delighted to have him here."