Killie won 2-1 at Rugby Park on Saturday but Shiels was dismayed by the decision to send off McKenna for a challenge on Borja Perez just two minutes into the game.
"The Football Association must have changed the rules on tackling and I don't know if there is a directive about tackling from UEFA," said the Killie boss.
"But I am trying to figure out what they are. I couldn't see anything wrong with the tackle and I would be very disappointed if I was Queen of the South."
Shiels drew comparisons with the previous week when Manuel Pascali was red-carded, a decision Kilmarnock unsuccessfully appealed against.
"It was almost a reversal of last week when Pascali was sent off for a similar kind of challenge and St Johnstone had the extra man," Shiels added.
"It hindered us as it gave us more space and time on the ball and we had too many options. There is nothing wrong with playing possession football but it needs a purpose.
"I am delighted, though, to get through and thought it was well deserved. We started last season's league cup run with a victory over Queens so who knows where we can go from here."
Unbeaten in the league and with cup wins over Hibernian and Rangers this season, Queens had high expectations of adding Kilmarnock's scalp.
Being reduced to 10 men for 88 minutes made it extremely difficult and when Cillian Sheridan guided a Perez corner into the net after eight minutes it was almost mission impossible for the Second Division side.
The Dumfries side got into their stride as they chased an equaliser but a second goal from Perez, who sidefooted the ball home from eight yards after a speedy counter-attack, should have killed off the tie.
Allan Johnston's men did not give up and when leading scorer Nicky Clark pulled one back with a brilliant diving header from a Ryan McGuffie cross high into the net the Queens made it a tense final 13 minutes.
But former Killie hero Johnston was denied a winning return and he felt that the sending-off handed his former club a huge advantage.
He said: "It was very frustrating. It is a hard job for referees but it just looked like a strong tackle to me.
"I didn't think it was a two-footed tackle and he has won the ball with one foot and maybe caught the player with the other. In my opinion it doesn't warrant a sending-off."
Johnston was delighted with his players' attitude after that early setback, particularly as they pushed for an equaliser in the closing stages of the game.
"To play against a top SPL side like Kilmarnock we didn't want them to pass the ball through us as they did last season and I thought we stopped them doing that in the middle of the park."