Owls winger Chris Maguire went closest for the home side with a deflected first-half free-kick against the crossbar while Rams substitute Johnny Russell was twice denied by Wednesday goalkeeper Keiren Westwood when clean through in the second period.
The result means both sides are unbeaten and have yet to concede a goal in their opening three matches of the campaign, registering two wins and a draw apiece in league and cup.
McClaren said: "Sheffield Wednesday are a far better team than last season, I don't think many teams will come here and collect points. I think they're tough opponents and I think, first half, we got a taste of it.
"We were on the back foot, we stopped playing football and credit to Sheffield Wednesday, their game plan was good and they put us under pressure and they probably felt at half-time they should have gone at least one goal up.
"We thought we got off the hook but second half we got more control.
"We toughed it out against a physical team, defended very well, looked hard to beat and we know we just need to improve at the other end. We nearly won it, I was pleased with the way we finished the game, the last 20 minutes we were very strong. I thought we were going to win the game then.
"We had excellent chances and you need to take them. We could, like we did last season here, have sneaked the win (a 1-0 success) and that's what you need to do.
"The performance was bitty, the back four and keeper were great but we need to get better.
"We know we've got players who can score and we've got to start doing that."
Owls head coach Stuart Gray was pleased with the performance of his players but felt they possibly should have taken all three points.
"It was two good teams both going for the win and I'm amazed it's finished 0-0," he said.
"I wanted a fast start and I just thought we nullified them really with the intensity and the hard work we put in.
"It was an entertaining 0-0 draw, I'm just disappointed that I'm not sat here talking to you about three points. I thought we had a 20-minute period in the first half where we probably dominated the game. But that's a quality side we've just played so the players should take a lot of encouragement from it.
"It just shows you how important goalkeepers are in your team; Lee Grant did very well for Derby and when Keiren Westwood had to pull off a save, around about the 80th minute, it was a big save for us.
"If I keep getting those performances from those 11 players I've put out, plus the subs, we'll win more games than we'll lose."