The home fans were left seething when Rankin made a complete mess of the best chance of the game late on. He was through on goal on his own after Ritchie Humphreys fell to ground, but hesitated for an incredibly long time and keeper Dimitrios Konstantopoulos gathered the ball with ease.
But Allen said: "I was hoping he'd put it in, but it was not to be. There will be no recriminations for him.
"We win together and take all the glory, but if players don't do it there will be no blame. Obviously he's naffed off.
"He's desperate to score and has been practising a lot on the training field. If he hadn't he would be in a bit of trouble.
"We were a bit unlucky not to win that game. We had the better chances, but we are still in the hat."
Allen had extra reason to curse his luck as Brentford also hit a post before Rankin's blunder.
Konstantopoulos watched helplessly as Jay Tabb's fierce shot from the edge of the area was deflected toward the corner on 62 minutes but came back off the post.
And Konstantopoulos pulled of the save of the game with just seconds left on the clock to stop sub Andy Frampton's piledriver.
But Hartlepool, who have failed to reach the fifth round in their history, deserved to take the game to a replay after coming close on a number of occasions themselves.
Hartlepool couldn't have got off to a much better start and laid siege to the Brentford goal in the first ten minutes.
Bees keeper Stuart Nelson had to be at his very best to turn Anthony Sweeney's 25-yard shot round the post.
Adam Boyd and Joel Porter were causing the Brentford backline all kinds of problems and the two combined thrillingly on the break only for Boyd's shot to be deflected over the bar.
The home side finally began to threaten through former Premiership striker Deon Burton and Hartlepool were relieved to see his volley go straight at Konstantopoulos.
Stewart Talbot also charged into the area only to blast his shot well wide from close range, but Boyd went close again when he volleyed over before the break.
Hartlepool faded after the break and only had a weak Boyd cross shot which was comfortably held by Nelson to show for their efforts.