The Owls were reduced to 10 men when Glenn Loovens was sent off in the second half, but Wildsmith said that his teammates deserve credit for their defensive solidarity.
"We dug in and also had a few chances and I thought we deserved a draw," BBC Sport quotes him as saying.
"The lads are up for it. We were very solid for the most of the game. It's credit to the boys and credit to the gaffer."
Wednesday occupy 16th place in the Championship following the derby stalemate, while United are 12 points better off in seventh.