A Michael Smith hat trick secured the points for the play-off bound visitors, whom, despite amassing 93 points with a game to play, will have to go into the end-of-season slugfest after wins elsewhere for Plymouth and Ipswich.
For Cotterill and Shrewsbury, there was certainly no shortage of effort in the penultimate home game of the season, and a couple of good spells of pressure and chances, but they just found Wednesday too hot to handle with their superior quality in attack.
“We always knew this would be a difficult game,” said Cotterill.
“There was plenty of effort, which is what we get always, but we have come up against a squad that is full of quality – and that’s it.
“What they have got is a squad, and, when it’s late on in a game, you are thinking ‘I hope he doesn’t want to come on and be a bit lively after we’ve already been going for 70 minutes’.
“They are just a side full of quality, and that is why they are on 90-plus points, which is normally enough to go up automatically.
“We haven’t got that quality, but the lads have tried and tried and tried and I certainly can’t fault them.
“We did give away a couple of poor goals, and they also showed their character, getting in four great blocks in the first half.
“Sometimes you can stand there and it doesn’t matter what you do, and what you change to, they just find a way on the pitch.
“The bottom line is they are a team that are just too good for us.”
Shrewsbury have also been hit by several injuries in recent weeks which have contributed to an eight-game winless run, and made it very difficult for Cotterill to find any sort of consistency in selections.
Striker Christian Saydee was restored to the starting line-up against Wednesday, but withdrawn at half time.
“It has been difficult for us to be fresh in recent weeks with the injuries we have had, and today was probably as flush as we have been with players, certainly for a little while,” added the manager.
“The trouble is then, some of them haven’t played much.
“If you take Christian Saydee, he has been absolutely first class for us.
“Maybe he will be better for the 45 minutes he has had today but he just wasn’t sharp.
“When we had those couple of moments that we had we need him to be sharp because we know what he can do.”
Shrewsbury will now be looking to respond to a current eight-game winless streak with a positive end to the season against Bristol Rovers on Tuesday and Lincoln next Sunday.
“We’ll be back in this week for these last two games and I know the lads will be committed right to the end,” added Cotterill.
“Everything feels like it is uphill at the moment and it’s been tough but we are also tough and we will see it out.”