Steve Davis insisted Crewe did enough to win at Gresty Road for the first time in three games after Shrewsbury emerged with a 1-1 draw.
The width of the crossbar denied Nathan Ellington the glory of making the swiftest of impacts on his debut as the Alex pressed hard in the closing stages of an intriguing derby battle.
Shrewsbury were a cut above Davis' side when they secured automatic promotion from League Two last season but the Railwaymen boss believes his men have adapted better to League One.
The current seven-point gap between the two sides backs that up, yet Luke Summerfield's first-half equaliser secured a point for Shrewsbury to add to their earlier 1-0 victory at the Greenhous Meadow.
"We were better than them and we have been in all three games and that's no disrespect to them," said Davis. "They were better than us last season even with Nick Powell and Ashley Westwood in our team. But we're a much better all-round team now and that performance was good enough to win the game."
The Railwaymen flew into a tenth-minute lead after some simple attacking play caught out a square Shrewsbury defence. Ajay Leitch-Smith slipped a ball inside for Byron Moore, who finished with aplomb, right-footed into the far corner.
Graham Turner's side appeared to have a realistic penalty appeal turned down after Rob Purdie was upended by Gregor Robertson before he could latch onto Tom Eaves' pass.
"Rob would have got onto the ball, although he might not have been in a shooting position," said Shrewsbury boss Graham Turner.
"If it had been against us I think it would have been a penalty. Four points from games at MK Dons and Crewe are a good return, especially in the position we're in.
"We've done quite well over a period of time when we've gone a goal down. We denied Crewe chances and we always looked a threat on the break. But we allowed them a bit too much room for the 15 minutes after half-time which could have been costly."