Rose were unable to add their name to the list of sides causing cup upsets as they went down 5-0 to Barry Ferguson’s cinch League 1 side.
Goals by inside the first 20 minutes by Mouhamed Niang and Euan Henderson had Rose up against it – and the hosts added three more in the closing 20 minutes, Henderson completing his hat-trick before Niang’s last-minute fifth.
Horn was naturally disappointed, but keen to move on as quickly as possible. And that means his main focus has already switched to this Saturday’s home league clash with Cumbernauld Colts.
Horn said: “I think we can play better. But everything I said last week - they've got to have an off day, we've got to be at out best and take our chances - we didn't do these things and ultimately they played well on the day.
"But we could have been 1-0 up after 15 seconds and if you score a goal at that stage the game's completely different.
"The disappointing factor was probably the last two goals. The game should have finished 3-0.
"We were naive in the way that still wanted to try and go forward and play but the game was done.
"But there's no embarrassment getting beaten by a team that was formerly in the Championship, guys that have played a a much higher level.
"We can't dwell on it. We move on and look forward to the game on Saturday which is miles more important.
"That was the message to the players after the game; we've got bigger fish to fry. We're in a great position in the league but we've got to keep that going."
Saturday’s opponents are one of only three sides to avoid defeat in a league match against Bonnyrigg this season, the sides drawing 0-0 at Broadwood in August – although the extreme 29 degree heat of that night is unlikely to be a factor at New. Dundas Park on Saturday.
"They've got good players so I'm surprised they are in the position they are. They're much lower down in the league than I would expect,” said Horn.
"On their day they can cause teams problems. We've just got to be wary but I think the next three or four games are massive for us.”