With Martin O'Neill again employing Gabby Agbonlahor as a lone striker, the Claret and Blue appeared toothless. However, the home side did have enough chances to grab a win which would have put them third.
With Manchester United and Arsenal playing on Sunday, Villa had a big chance to put real pressure on one half of the top four.
But, as is so often the case at Villa Park, the home side lacked a cutting edge and clearly missed John Carew.
Agbonlahor was forced to shoulder the burden of holding the ball up and waiting for support as James Milner and Ashley Young failed to provide enough assistance.
Gareth Barry and Steve Sidwell looked most likely to break the deadlock as they worked tirelessly in box to box midfield roles.
Villa failed to get a shot on target in the first half as Barry missed a glorious headed opportunity, which drifted just wide of Mark Schwarzer's upright.
Sidwell was also guilty of profligacy as he guided a free header over the bar with the Fulham keeper stranded.
Hodgson's side lacked enough ingenuity to trouble their hosts and looked content to gain a second successive away point after their goalless draw at Liverpool last weekend.
Fumbled
They managed to test Brad Friedel once in the second half via the right boot of American Clint Dempsey but it was Villa who dominated after the break.
Unfortunately for the frustrated home fans, the Villans failed to make their corner count truly count despite troubling the nervy Schwarzer.
The Aussie keeper almost contrived to give Villa a goal as he fumbled a Barry header onto the bar and struggled to claim high balls.
Fulham had not claimed a victory at Villa Park in 35 years and with the away side posing few threats on the break Villa upped the ante.
But, despite peppering the Holte End goal with balls into the box there was no one to get on the end of the supply leaving many wondering just why O'Neill failed to utilise any of his seven substitutes.
Marlon Harewood, in particular must now be thinking of a move away from the club after he wasn't given the chance to claim a Villa victory.
All in all it was another frustrating encounter for Villa fans, who have only seen one goal in their side's last three home games.