Blues created a number of chances but were not quite clinical enough to put the ball in the back of the net against an Owls side that were unbeaten in their previous five matches.
"It was a tough game and both teams had a right good go at each other," said Clark. "Overall we probably felt we had done enough to have won it.
"I'm very happy for the players in keeping a clean sheet for the first time in a long time. I think they've been unfortunate in the last few games where we could have had those types of situations. Certainly at Huddersfield away when we were 40 seconds away from getting a 1-0 there and we've also had a good shape against Watford. When you keep a clean sheet it always gives you an opportunity with the attacking players we have to win the game.
"But everyone stuck to the game plan tonight and we knew what was coming from Sheffield Wednesday and every single player has made a contribution. Hopefully we can take that onto Saturday now."
Blues had goalkeeper Jack Butland to thank for a pulling off yet another world-class save to deny Miguel Llera in the first half.
"It was a terrific save from Jack," acknowledged the Blues boss. "It's a bit of a sad statement really but it's something you come to expect from him because he's that good. You shouldn't really expect it but because his standards are that high you are not surprised when he does it.
"I think that apart from that he had lots of basic things to do in terms of coming for crosses. He had to be strong and brave because they are a big side that make it difficult for goalkeepers but he dealt with it brilliantly."
Clark made five changes to his starting line-up and he admits it was a difficult decision leaving so many players out.
"To be fair to the lads that were left out tonight it was a bit of a tough call because even though we'd lost 4-0 on Saturday it was because of individual errors and getting hit on the break," he added. "We didn't lose because we weren't at it.
"But I thought the other players that came back into the fold like Nikola Zigic, Marlon King and Jonathan Spector made a big difference, and the two local boys (Callum Reilly and Mitch Hancox) did great.
"What the group are doing now is showing me they're giving everything. As long as we keep that going it's one defeat in seven for us and we keep moving forward and progressing."