The Latics won with a 13th-minute goal from Jonathan Grounds, who slotted home from six yards after goalkeeper Chris Weale palmed out Matt Derbyshire's low cross.
It was their second of the week after a 2-1 victory at rock-bottom Hartlepool on Tuesday night. It moved them towards a mid-table position and brought relief for Dickov.
"After losing at Bournemouth last weekend we knew how important it was to take six points from the next two games," said the Scot. "We haven't been the best football-wise, either here or at Hartlepool, but we've shown a lot of effort and endeavour.
"We were on a bad run, so it was important to regroup and stress to the players that we always have to show the right attitude. You have to do the ugly things well, and that's how we've managed to get these results. I'm particularly pleased with the clean sheet and I thought our two centre-backs did a good job against their strikers.
"I knew this would be a battle because Shrewsbury played ever so well against MK Dons the other day when their front four were a proper handful. Too often this season I've talked about us playing well after we've lost the game. This was all about the result, so it's pleasing that we've ground out all three points."