Veteran centre Shanklin took a knock to the head in the 18-17 victory at the Cardiff City Stadium, while loosehead prop Jenkins rolled his ankle.
"Tom took the ball up and collided with two or three players and took a bang on the head," said Young, who was quick to calm fears that the Welsh duo could face a spell on the sidelines.
"We took him off as a precaution.
"Gethin went off after he rolled his ankle again. We are hoping that it is nothing too serious and he was limping about after the game. We don't think he needs an x-ray or a scan.
"We should know where the both of them are and have a clearer picture on how they are on Monday."
Having won the Amlin Challenge Cup last term and started the Magners League with four wins from five, the Blues have been heavily tipped for more success this season.
Saturday's opening encounter reminded Blues fans of the need not to get carried away as Edinburgh almost secured an upset but, despite the nature of the performance, Young believes the four points gained could prove vital in their quest for European progression.
"We know we didn't play as well as we would have liked. But Edinburgh have always caused us problems and they certainly did that in this game," added Young, whose side beat Edinburgh 34-23 in the opening round of this year's Magners League season.
"I don't think we played anywhere near our potential but I thought we showed a lot of grit and determination to come away with a victory.
"We tried to play and we had a couple of really good opportunities where a pass outside meant a tackle and a pass inside meant a try.
"But I thought the determination and attitude was there for everybody to see, even though we were nowhere near how we can play.
"Hopefully, we will look back at this and say it was a very important win."
63x46.png){kind=logo}