Both sides lacked the quality to make the breakthrough on Saturday, with the hosts guilty of squandering good chances through John Arne Riise, Bobby Zamora and Andrew Johnson.
That was partly down to an impressive debut for new Villa goalkeeper Shay Given who, along with fellow new boy Charles N'Zogbia, was one of few positives in new manager Alex McLeish's first competitive game in charge.
Europa League participants Fulham also failed to make the most of having played six competitive matches already this season, something which was expected to help them make a fast start in the Premier League.
Saturday's contest was therefore thought to be a baptism of fire for McLeish, who needed to hit the ground running to silence the doubters following his controversial defection from Birmingham.
There was no shortage of backing for either side early on from fans optimistic about a new season.
The home support should have been given something to cheer in the 10th minute when Danny Murphy poked a ball through for the unmarked Riise, who blazed over with the goal at his mercy.
Villa were playing an interesting 4-2-3-1 formation, with £9.5million man N'Zogbia, Emile Heskey and Gabriel Agbonlahor playing just off Darren Bent.
But they were lacking penetration, as well as the imagination to try something unexpected, unlike Fulham's Damien Duff, who volleyed over right-footed for 25 yards.
The visitors were almost gifted a 20th-minute opener when Richard Dunne pumped a hopeful ball down the left and Philippe Senderos lost track of Heskey, who volleyed straight at Mark Schwarzer.
Murphy then earned the game's first booking for an ugly scissors tackle on N'Zogbia, while Bent had the ball in the net midway through the half but he was well offside.
Villa were starting to create and an unmarked Heskey should have headed N'Zogbia's right-wing cross on target, with the ball appearing to screw off the former England striker's shoulder.
N'Zogbia apart, there was a distinct lack of quality in the final third from both sides, and the Frenchman was next to produce a telling ball when James Collins powered over a header under pressure.
Villa captain Stiliyan Petrov then went as close as anyone with a 35-yard piledriver which flashed just over.
A goalkeeper was finally called into significant action four minutes before the break when Johnson cut inside Collins and blasted straight at Given.
Agbonlahor was booked, seemingly for delaying a free-kick, moments before half-time.
Bobby Zamora had been largely anonymous before the interval but he exploded into life within a minute of the restart, reading Johnson's flick-on from Duff's ball and lashing a shot straight at Given.
Dempsey nodded over the rebound but Zamora was soon at it again, glancing Riise's cross too close to the goalkeeper.
It took almost another 20 minutes from the next chance to arrive and again it fell to Zamora, who took Murphy's crossfield ball out of the air and left Stephen Warnock on the deck before his shot was closed down by Given.
Johnson had an even better chance moments later but he scuffed his shot too close to the goalkeeper.
Villa needed something different, although it was a surprise to see N'Zogbia withdrawn for Marc Albrighton.
Yet, the youngster's introduction almost proved a masterstroke when he flashed Bent's cutback into the side-netting with 15 minutes remaining, Villa's first shot of the half.
Fulham had already sacrificed Zamora for Mousa Dembele but the visitors were in the ascendancy and Dunne's header from Fabian Delph's corner was deflected narrowly wide.
With time running out, there was a flurry of yellow cards for Petrov, Dembele and Dunne as frustration grew on both sides.
Villa threw on Ciaran Clark for captain Petrov in the final minute, but far too late to have any effect.