Barnsley's Clarke Oduor went close to scoring a fine individual goal, producing a mazy run into the area before firing in a shot which was saved by Thomas Kaminski.
Michal Helik directed a header on target after meeting a corner from Cauley Woodrow, but Kaminski was able to make a comfortable save.
A powerful run from Helik saw him upended before he was able to reach the D and the resulting free-kick, taken by Woodrow, was deflected wide off the defensive wall.
Kaminski made a great save to keep out Frieser's header following a corner.
Blackburn also went close soon afterwards when Ben Brereton Diaz found himself through on goal, but he was denied by Brad Collins who came to his side's rescue with an important block.
The home side went desperately close to scoring when Helik's flicked near-post header just evaded the stretching Victor Adeboyejo and the ball went a fraction beyond the far post.
Both sides went in search of a late winner, with Barnsley's Callum Styles putting a 30-yard drive wide before Collins was forced to save an effort from Clarkson, who was set up inside the area by Reda Khadra.
Schopp said: "I think it was not a good game from both sides. It was the third game in a week for us, but I'll not use this as an excuse. Even the weather probably had a bit of an impact.
"We needed an opener for the game and Clarke Oduor had a big chance for us, but it didn't happen.
"We had a bit more chances than them, but they were really, really dangerous in the transition moments and we gave too many easy balls away. Fortunately, we defended well.
"In the second half we had more but it didn't work out. It's all about knowing what we have to do better, and we know that we can do a lot better.
"A couple of players will be coming back next week so the competition will be getting bigger.
"We have to take this point, but we wanted to take more today."
Blackburn boss Tony Mowbray said: "We worked hard and denied them many opportunities. There was one clear-cut when he was through on goal and the keeper made a good save.
"Apart from that, I thought we restricted them pretty well. I think if either team had the better opportunities, it was probably us and yet we didn't take them today. We weren't as clinical as maybe we'd like to be.
"The team worked hard and looked organised. It's always a tough place to come to, particularly with the fans back in.
"I still thought right to the end we could win it. I thought we looked dangerous, as they did. They flood men forward when they win the ball back in midfield and they've got some good players. Woodrow, with his back to goal, is an exceptionally good player.
"We take the point and we move on. It's four games unbeaten this season away from home. We would like to be sitting here having won 1-0, but we'll take the point and look forward to Cardiff next week."