Craig Levein admitted Marco di Marchi's red card helped send Dundee out of the Tennents Scottish Cup.
The Dens Park side spent an hour of the fourth-round replay down to 10 men after di Marchi was given his marching orders.
Levein conceded that the sending-off did make it easier for Hearts to progress in the competition after an evenly-matched contest.
He said: "I said to the players that I didn't see the incident - just that the linesman's flag was up.
"Colin Cameron was unjustly sent off on Saturday and I felt that that turned the game for us.
"I felt them having a man sent off certainly helped us."
Robert Tomaschek grabbed the only goal of the game when he nodded past goalkeeper Marco Roccati after 71 minutes to book Hearts a trip to Parkhead to take on Celtic in the quarter-final after they dumped Dunfermline out of the Cup.
And Levein admits tackling Celtic's 100 per cent home record is going to be a difficult task.
He added: "It was a great finish from Robert. He's been getting to the back post a bit more and we've been having a smile about how often his hits the target.
"We are going to Parkhead and the only people expecting us to have a chance are ourselves.
"For any club to go to Parkhead it is going to be rewarding financially but that doesn't concern me or the players - what does concern us is getting through the game.
"If we get through it will be a remarkable achievement. Celtic are undefeated at home and that's a hard enough task to think about."