Thistle found out they would be facing the Dons in the fourth round of the competition the day after suffering a 4-0 thrashing to Derek McInnes' men.
As well as Monday's reverse at Pittodrie, the Jags also lost 3-0 to Aberdeen in the Scottish Premiership at Firhill earlier in the season.
And Archibald says a cup rendezvous with their two-times conquerors was not the draw he was hoping for.
He said: "Certainly not, considering the fact our two heaviest defeats were to Aberdeen.
"Not only that, in the Scottish Cup, you like something a bit different.
"When we were in the First Division, we wanted a Premier League team or someone from outside our own league.
"We didn't get that this time. But it's a home tie so that should be a bonus."
Archibald is now hoping for a positive response to the defeat when Partick host St Mirren this weekend.
He said: "We were back in the day after and we had a chat about it then.
"We've got it out of our systems and we move on now to Saturday's game. It's a massive game for us.
"We had a good performance at their place earlier in the season and another performance like that would hopefully see us take the three points.
"We know it will be a very hard match. It will be a different St Mirren team from that game.
"They are a lot more confident and you could see that last week against Ross County."