Neither side could find a breakthrough in a lacklustre game at Hillsborough, which ensures that the tie will be replayed at the Liberty Stadium.
While Owls boss Luhukay is pleased to still have the chance to reach the quarter-finals, he admits that having a depleted squad makes the prospect of an extra fixture "difficult".
"We didn't want a replay because we have so many games and lots of injuries," the Dutchman told BBC Sport. "But we are still in the FA Cup and have a chance to get to the next round.
"First half we were the better team and in the second half Swansea were better so in the end it is a draw which both teams must enjoy.
"I'm proud of my team. We played the first 25-30 minutes good and we were direct from the beginning. The first half we played good football but couldn't score a goal.
"We have a difficult situation and a very small team now [because of injuries]. Most of the time it is difficult, getting 20 players day to day but we have positive thinking."
Wednesday return to Championship action on Tuesday night with a trip to Millwall.