On 24 minutes Crofts shot straight at Alnwick, and full-back Bruno Saltor saw a shot well blocked by Rhoys Wiggins two minutes after.
Coleman, following slack Italian defending, saw a shot blocked by Angelo Ogbonna while the outstanding Hendrick dragged another effort wide.
Ermir Lanjani, making inroads with his persistence on the left, saw a shot deflect off Patrice Evra.
He saw a shot deflect narrowly wide and he hit the crossbar with a header from Marc Albrighton's corner.
Mahrez saw a shot deflect wide off Kaboul but eventually doubled Leicester's lead on 18 minutes when he powered in a 12-yard header from Albrighton's cross.
The Spain striker headed over after four minutes, saw a shot deflected off target shortly after that and had a third effort saved by Deportivo keeper Daniel Aranzubia.
Miller soon saw a shot deflected just wide after a lay-off from Nish, whose header from the resulting corner was parried wide by Crawford.
Shrewsbury, third-round conquerors of Cardiff, enjoyed plenty of possession but chances were hard to come by, although Junior Brown saw a shot deflected off target.
Vieri somehow missed from six yards in the 90th minute and Gennaro Gattuso saw a shot tipped over in extra-time.
Ronaldo saw a shot flash wide, a free-kick dip past the post and just before half-time he appealed for a penalty.
The Villa substitute Jordan Ayew saw a shot deflected shot before the recalled Westwood, in space on the edge of the area, drove over.
