These are the occasions I can find where we've gone into the last match able to either make the finals or not make the finals:
1984, Brandy's first year, needed to win at home against Parra (3rd) to make clear 5th. Result- Lost 22-10. It was a champion Parra team going for 4 straight premierships though. It was a dead rubber for Parramatta as they could only finish 2nd or 3rd. They would end our season the following year as well.
1985: Went into the last round against Easts (who also had a slight chance of making the finals) level 5th with Manly and trailing them in F/A by 4 points. In a tremendous performance in front of 8,000 (I was one of them) fans at the Sydney Sports Ground, Alexander (who soon after would become the club's only winner of the Dally M Medal) plucked the Roosters and we won 38-6. I remember Roosters fans shouting out not to give the ball to Col Drier, who apparently had a shocker. Manly won too, and so the historic match at the SCG midweek when we beat Manly in extra time. All to no avail, as Parra would again snuff out our season by the same score as the Easts game. Predictably so, as the celebrations after the Manly game were more like a team who'd won the GF, which making the top 5 was for our blokes at the time.
1988, Lost last two against Balmain and Manly to be forced into 5th place playoff against Tigers (who went on to lose the GF), lost that too. Again two very strong sides.
2013- Went into round 26 with the barest mathematical possibility, but thats all. We'd been going well a few weeks earlier but a few hidings killed us off. In the event, although we beat Manly at Brookvale in the final game, we would have had to make up almost 100 points in F/A on the Cows, even if they had lost, which they didn't. We had lost 8-6 to the Knights in Newcastle in a very poor quality round 6 game where we got the raw prawn from Badger and Perenara, if we'd won that we would have made it. Then there was the Tigers game when the NRL ordered the club not to play Matt Moylan. But we'd been getting belted badly by the better teams anyway.
2009- Once again went into the final game with the slimmest mathematical chance, and were hammered by the Knights 35-0. This is the game I like to think of when feeling sorry for the Knights in more recent times.