Fredy Guarin put the home side in front with a first half strike but Andi Lila sealed a point for the struggling visitors
Despite dictating much of the play, Inter lacked fluidity in the opening period and were fortunate to take the lead, as Fredy Guarin's long-range drive struck Jose Mauri on its way into the net.
The hosts had been hoping to boost their dwindling European hopes with victory, though they were consistently wasteful in front of goal in the absence of injured top scorer Mauro Icardi.
Without him, Inter lacked potency in the final third and allowed Parma to claw their way back into the contest with an equaliser just before the break when Lila nodded past Samir Handanovic.
Roberto Mancini's side continued to dominate after the break and saw chances fall to Croatia pair Mateo Kovacic and Marcelo Brozovic, but failed to break down Parma's resilient backline.
Two notable inclusions were present in Inter's line-up, as Felipe – who was released by Parma in February – was given his club debut, while 18-year-old striker George Puscas made his first Serie A start.
But service to the young Romanian during the early exchanges was in short supply, with Parma crafting the first opportunity in the second minute, as Handanovic kept out Silvestre Varela's long-range drive.
Inter eventually came to life in the 14th minute, with Xherdan Shaqiri's first-time effort forcing Antonio Mirante into action after a precise cut-back from Rodrigo Palacio.
The Parma goalkeeper was rendered helpless 10 minutes later, though, as Guarin's audacious effort from 35 yards took a hefty deflection off Mauri and squeezed inside the right-hand post.
Inter failed to fully capitalise on their dominance, however, and they went into the break level.
Varela clipped a teasing delivery into the penalty area from the right and, after breaking free of Gary Medel, Lila guided a fine header into the top-left corner with just a minute left of the first half.
Mancini introduced Kovacic for the anonymous Puscas at half-time and he almost made a telling difference in the 53rd minute when he headed Juan Jesus' cross just wide of the target.
Kovacic's compatriot Brozovic was the next to go close for Inter, smashing just past the post from 25 yards 13 minutes later, as the hosts' frustration grew.
Inter piled the pressure on towards the end and almost snatched the points in dramatic fashion three minutes from time, but Palacio failed to get meaningful contact on Shaqiri's devilish cross and Mirante grasped it gratefully as Parma held firm.