Shrewsbury Town boss makes Sunderland claim in verdict on Stadium of Light defeat
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Wilbraham is in charge while Steve Cotterill continues his recovery from COVID-19, and oversaw a much improved second-half showing.
Sunderland dominated the opening half hour, and had opportunities to extend their lead further after Charlie Wyke's fine early header.
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Hide AdA missed chance from Leon Clarke represented something of a turn in the momentum of the contest, and Shrewsbury were the better side for much of the second half.
"I think we definitely deserved something out of the game," said Wilbraham.
"Sunderland started bright, we knew they would, and we matched them for effort but we didn't settle down on the ball as we usually would.
"For the last 15 minutes of the first half and the whole of the second we were pretty much camped in their half," he added.
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Hide AdWe had a few decent chances, if one of those goes in it's a totally different game. If you spoke to the Sunderland coaching staff - they said it themselves - they were lucky to get all three points. We deserved to get something."
The contest was Shrewsbury's first league game of 2021 after the COVID outbreak at the club, and though they remain just three points above the relegation zone, Cotterill's arrival proved to be a catalyst over the festive period.
Shrewsbury had won four of their last five before Saturday, including wins against Hull City, Lincoln City and Doncaster Rovers.
"We will recover and we get the chance to start a new run of league games now," Wilbraham said.
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Hide Ad"The unbeaten run comes to an end but we go again and start a new run. We take the positives from the second half into Tuesday.
"I told the lads no-one feeling sorry for themselves or heads down, because they can take a lot from that second half."
While conceding that his side had been too 'frantic' in the second half, Sunderland head coach Lee Johnson also praised their defensive resilience.
Though poor in possession, Sunderland's defence gave up few clear chances and goalkeeper Lee Burge largely went untested aside from a fine save to deny Harry Chapman in the first half.
"In the second half we had to dig in,” he said.
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Hide Ad"They made it a battle, we made it a battle at times and that's something we've got to look at.
"I don't think we were ever under massive threat, there was a bombardment of the box from long throws and a couple of wide free kicks, but I thought we were solid and very strong in the middle of the goal.
"I did think we dealt with the pressure well defensively, we changed the formation which you don't want to do where possible but I felt we needed some strength in the middle of the pitch, and that sacrifices the forward play a little.
"The bit we did do quite well was manage the last six to eight minutes well, because that's not easy and we saw that out well."