The Scottish Cup holders made the better chances in a nervy match but lacked a cutting edge up front and the hosts hung on to see out a goalless draw, meaning they progress to the third qualifying round with a 1-0 aggregate win.
Trailing by one goal from the first leg, Inverness made a slow start to the return game and enjoyed plenty of possession without troubling their opponents at first.
Indeed, the closest they came initially was with a wayward 35-yard free kick from Greg Tansey which flew well over the crossbar and Astra appeared happy to absorb pressure.
Caley Thistle soon made better openings and David Raven cut inside from his unfamiliar left-back position to shoot just wide from 22 yards.
Gary Warren also challenged goalkeeper Silviu Lung but he managed to hold the ball before Aaron Doran was denied and Ryan Christie had a goalbound shot tipped over.
Tempers were starting to flare and it was crucial for the Highlanders to keep their discipline as the second half began because questions were being asked of Astra.
The hosts reacted by raising the tempo after the restart in order to get a goal which would virtually put them through.
Inverness continued to press though and only offside flags prevented Doran and Lopez from catching sight of goal.
Constantin Budescu hit back for Astra and Welsh squad member Owain Fon Williams had to be alert to keep him out with an excellent stop.
Play was opening up and the Romanians were coming into the game more as they forced a number of corners and stretched Hughes’ men.
But Doran missed a great chance with 15 minutes to go as he homed in on goal only to scuff his shot and shot straight at Lung.
With time running out as they looked to at least force extra-time, the Scottish Premiership side threw more players forward in search of a goal.
It never came, however, and despite a good performance on the night, Inverness’ first foray into European competition came to an end at the first hurdle.