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The Icelandic striker bagged a double to inflict defeat on the Welsh side, ensuring a third successive home win for Tony Mowbray's side.
Parkinson credited Rovers for their defensive work, restricting Wrexham to few efforts on goal.
“Difficult conditions for both sides. We were against it a bit in terms of elements first half," Parkinson reflected.
“Obviously conceding just before the break was a setback but we still felt at half-time the game was there for us. But we couldn’t produce the quality we needed.
“We’ve had 23 attempts but to only have one of those on target, we have to look at that.
“I’ve got to give Blackburn defenders credit because they blocked things, made 9-10 blocks. They defended crosses, they defended set plays. It was a combination of their good defending, but we couldn’t find that clinical moment to get us back in the game and the game was separated on two moments.
“When we analyse the positions we got into, we got in enough good positions to have got something from the game but we just didn’t produce the quality.”
(Image: CameraSport - Lee Parker)
The experienced boss believed that Rovers' number nine and his clinical finishing was the difference in the game.
“Gudjohnsen is what separated the teams today. The first goal was a quick reaction, and that was it," he said.
“I can’t fault our team’s effort, we gave everything. Set plays at times were good, but as the game went on and after making changes, the delivery wasn’t as accurate.
“First half, we were in brilliant positions on that right side with Issa [Kabore], we had shots blocked, Kieffer’s header from the corner.
"We had enough moments in areas where we could exploit Blackburn where they have conceded in recent weeks, but I’m sure Tony [Mowbray] will say his defenders stood up and were counted today, in the important areas of the pitch in the penalty boxes.
“When we review the game, we’ll see we got into enough good areas, the approach play that we worked on in the week was really good, but football is all about taking the moments.”