Aberdeen made the competition's final four with a 1-0 win over St Johnstone, with Adam Rooney heading home a late winner for the Dons on Thursday night.
Now the Pittodrie side will come up against Morton, the club McInnes spent seven years at as a player.
"When [Celtic and Sevco] are in the draw along with a team from the Championship, we probably all want the Championship team - but Morton probably wanted us as well, I would imagine," said the Aberdeen boss.
"But that is with the greatest respect to Morton because they are my club really.
"Some of my fondest memories in the game have been there and I have got a huge attachment to the club so I am so pleased that they are in the semi-final and pleased for Douglas Rae and Jim Duffy down there.
"Lots of my friends are Morton supporters so I am delighted I will get the chance to put myself up against them, but that will be a tough game."
Source: STV