Rovers were left to rue missed opportunities as they missed the chance to make the end of season promotion play-offs.
Damien Johnson's side knew that victory would have ensured a top-five finish, but they were found wanting in front of goal at a bitterly cold night at Ewood Park.
The first half saw Rovers miss a host of chances as Connor Thomson, Lewis Mansell, Daniel Butterworth and Joe Rankin-Costello all failed to threaten the Villa goal. Willem Tomlinson would go the closest but his 25-yard free-kick smacked the post.
Villa had more joy in the final third in the second half, but a combination of good goalkeeping from Andy Fisher and their own inability to hit the target ensured the game finished goalless and with it a frustrating end to the league campaign for both sides.
The two teams went into the match at Ewood Park knowing that victory for either of them would guarantee that their season would be extended, but the first half was certainly case of untaken chances.
It was the visitors with the first sight in front of goal after just four minutes. Callum O'Hare with a ball into Keinan Davis who shot first-time but Rovers keeper Fisher made a sublime one-handed save at his near post to keep out the effort.
On nine minutes Rovers worked the ball well through to Butterworth, but instead of going for goal himself he passed to Thomson but the midfielder shot tamely into the arms of keeper Matija Sarkic.
Villa went straight up the other end as Corey Blackett-Taylor played Jordan Cox in on goal, but Fisher was there again to get enough on the ball to prevent it from finding the target.
After that it was largely one-way traffic towards the opposition goal, but with Rovers spurning chance after chance to go in front.
Butterworth stabbed an effort straight at Sarkic after being fed by Mansell, before great forward play saw Tomlinson advance, he found Rankin-Costello who rode two challenges but he could only fire over from 20-yards.
But at the midway point of the half Rovers really should have opened the scoring. A deflected pass saw the ball at the feet of Mansell in on goal, but with just the Villa keeper to beat he put his effort wide from six yards out.
Rovers continued to press, Tyler Magloire was just a whisker away from reaching a Lewis Hardcastle corner, then after Rankin-Costello had been fouled, Tomlinson struck the foot of the post with a 20-yard free-kick.
The last action of the first half saw another Rovers chance go begging. Hardcastle showed good awareness to intercept a poor pass from defender Jacob Bedeau. He played the ball in to Rankin-Costello who cut inside onto his right foot but could only bend his effort over the target.
Like the first half it was the visitors with the first effort at goal in the second. A corner from the left reached Easah Suliman just six yards out, but he stood on the ball and that allowed Rovers to clear.
The home side raced up the other end with Thomson crossing from the right, it beat everyone in the centre, but as young defender Lewis Thompson raced into the box, his curling shot was headed off the post to safety.
Then just before the hour mark the Rovers fans in the Jack Walker lower thought Rovers had finally broken the deadlock when Butterworth let fly, but his curling effort just grazed the side-netting as it flashed the wrong side of the upright.
That prompted a double change from the visitors as Kelsey Mooney and Jack Clarke were introduced, and that brought about a change of momentum as Villa started to look the stronger side.
A cross from the left picked out forward Davis on 67 minutes, but with Fisher stationary, he planted his header wide. Then it was the turn of sub Mooney to get in on goal, but again Fisher saved well, getting down low to his right to push the ball behind.
The game became stretched in the closing stages with the visitors much the better of the two sides.
Mooney spurned another chance when he headed wide, before Villa saw appeals for a penalty waved away as the ball appeared to strike a Rovers arm in the box.
In time added on at the end of the match Villa threatened twice further. First a shot from O'Hare was blocked into the path of Davis but Fisher pounced on the ball. Before Mooney was played in on goal but with just the keeper to beat he fired wide of goal.
It was a dramatic end to the match, but ultimately it was a result that neither side wanted as West Ham United grabbed the final play-off place thanks to their 4-0 win over West Bromwich Albion.
ROVERS: Fisher, Travis, Thompson, Tomlinson, Magloire, Grayson, Thomson, Hardcastle (c), Mansell, Butterworth, Rankin-Costello.
Subs not used: C. Doyle, Powell (GK), Mols, Wright, Evans.
Booked: Magloire 63 mins, Hardcastle 80 mins
VILLA: Sarkic, Walker (sub Finnerty 72 mins), Leggett (c), Hale, Suliman, Bedeau, Blackett-Taylor (sub Mooney 60 mins), O'Hare, Davis, Doyle-Hayes, Cox (sub Clarke 60 mins).
Subs not used: Watkins (GK), Knibbs.