© PA Photos
Esteban Granero looked to give the visitors an early lead with a free kick from just outside the penalty area, but his curling effort was kept out by the crossbar.
Adel Taarabt showed strong pace, breaking into the box twice in five minutes, but he failed to find the target with his final touch.
The home side applied some pressure towards the end of the opening period, as Pavel Pogrebnyak forced a save from Rob Green before Jose Bosingwa cleared the ball off the line, and referee Kevin Friend turned down two penalty appeals.
Harry Redknapp's side made a strong start to the second half, but Taarabt scuffed two shots to give McCarthy a couple of easy saves.
Pogrebnyak had a good chance for Reading in the 60th minute, as the Russian looked to curl the ball into the top right corner, but the effort was just off target.
Green had to be on hand to stop a Danny Guthrie strike moments later, as Granero allowed the midfielder through on goal.
There continued to be chances at either end, including a Sean Morrison header inside the final five minutes, which needed swift action from Green to prevent Reading from taking the lead.
Both teams pressed hard in the closing minutes of the match, with chances at either end of the pitch, but neither could break the deadlock.
The result sees both teams relegated from the Premier League, as the sides above them, Aston Villa and Wigan Athletic, are yet to play.