Ronnie Moore praised his high-flying Tranmere side for never giving up after a late equaliser from Jean-Louis Akpa Akpro preserved their unbeaten start to the season.
There were just two minutes remaining when Akpa Akpro levelled matters at 1-1, cancelling out Marvin Morgan's powerful header from a Mark Wright free-kick on the stroke of half-time.
Tranmere were indebted to an outstanding display from goalkeeper Owain Fon Williams, crowned by two fine stops in stoppage time from Asa Hall and Michael Hector.
Moore said: "We never started until the second half. For 45 minutes we were never in the game which is not like us and we looked tired.
"We had one or two words at half-time and I think second half we came on. It was a good game.
"There was a lot of effort and determination and it was great to get the goal at the end. We might have pinched it at the end as it was a great ball in from Andy Robinson which went unconverted."
Shrewsbury boss Graham Turner, whose team are unbeaten in their last 34 home games, admitted he was frustrated his promoted side were unable to hold out for a second 1-0 win of the week at the Greenhous Meadow.
"It's bitterly disappointing, particularly to concede one as late as that," Turner said. "There were times when we didn't want it to be end-to-end. We just wanted to kill the game off but it was like that for a period.
"I thought we should have killed them off and we had one or two great breaks when we should have picked a better ball out. Then their keeper's made a great save at the end.
"In some ways we can count ourselves a little bit unlucky, but in other ways there was a little bit of naivity about our play. We should have defended better late on."