Gianluca Caprari gave Pescara a shock 14th-minute lead at the Stadio Olimpico and although Roma got back on level terms at the start of the second half through Mattia Destro, the home side could not force a winner.
The result leaves Roma in sixth place, a point behind Inter Milan who climbed into the top five with their 1-0 win over Parma earlier on Sunday.
Roma came into the weekend with confidence high after beating Torino away in Serie A last Sunday and then completing a 5-3 aggregate win over Inter in midweek to reach the Coppa Italia final, where they will meet bitter rivals Lazio next month.
Roma coach Aurelio Andreazzoli warned his players not to get distracted by that derby clash ahead of the visit of Pescara, but that appeared to fall on deaf ears as Serie A's worst team enjoyed the better of the early exchanges.
Ferdinando Sforzini spurned a good chance in the opening two minutes when he fired high over the bar with only Maarten Stekelenburg to beat, but Pescara were celebrating the lead 12 minutes later thanks to Caprari.
Manuel Cascione's shot from outside the area was parried by Stekelenburg and Caprari was quickest to the loose ball to head into an empty net.
That seemed to spark Roma into action and Alessandro Florenzi missed two chances to get his side back on terms before the break, seeing Pescara keeper Ivan Pelizzoli save his first shot and then later on fluffing another opportunity from close range.
Francesco Totti also failed to make the most of his chance in first-half stoppage time as Pescara went into the interval still ahead.
Their lead lasted only six minutes of the second half though before Roma drew level through Destro, who slotted home after a free-kick into the box had led to a goalmouth scramble.
With almost the whole second period left, Roma must have fancied their chance of finding a winner.
However, Totti, Daniele De Rossi and Destro were all denied by fine saves from Pelizzoli while Destro saw another effort go inches wide as Roma were thwarted.
The home side might even have ended up suffering a shock defeat as well, with Stekelenburg doing well to prevent Sforzini capitalising on a mistake by Roma defender Leandro Castan before the Holland international produced a brilliant save to keep out Federico Di Francesco's superb late lob.