Leonardo Ulloa's late winner for Brighton & Hove Albion against Nottingham Forest meant the Royals were pipped to the final playoff spot in the last few minutes of the Championship season.
The home side had their lead on 16 minutes when they broke from a Burnley corner and the counter-attack was eventually finished off by Kieran Trippier, who could only guide the ball into his own net as he tried to clear a cross.
However, the Clarets were back in it moments later when Scott Arfield turned home his eighth strike of the campaign after Reading failed to clear a low cross.
Hope Akpan drilled a fierce effort into Shackell's legs after the visitors again failed to stop the ball coming in from a wide area, before Tom Heaton had to be alert moments later to deny a second own goal from Michael Duff.
Danny Ings gave his side the lead just before the half-hour mark when he netted his 26th goal of the campaign with a sharp turn and strike on the edge of the box.
The home side equalised shortly before the hour mark when Gareth McCleary steered a 25-yard volley into the corner to give Heaton no chance in the Burnley goal.
Pogrebnyak nearly made it safe on 75 minutes but his left-footed effort was cleared off the line by Shackell with Heaton beaten.
McCleary raced through seconds later for his brace, but his low shot was saved by Heaton's outstretched foot.