Serbia's substitute keeper Damir gave away the spot-kick after coming on at half-time to replace Branimir Aleksic whose fumble at a corner allowed Ola Toivonen to give Sweden the lead before Neven Subotic equalised for the Serbs with a header.
Sweden, who face co-hosts Ukraine in their Group D opener in Kiev on Monday, controlled the early stages and Sebastian Larsson nearly scored in the fifth minute from 35 metres after Aleksic cleared the ball straight to him.
Sweden's Andreas Isaksson made a fine double save following a Zoran Tosic free-kick just outside the area but Serbia levelled from the resulting corner with a fine Subotic header - the third headed goal the Swedes had conceded in two games.
"That shouldn't be allowed to happen [conceding from a corner]. It's now we can make mistakes and now everything can go wrong - it can't be allowed to happen in six days' time," he said.
"It's easier to correct if it happens at a dead ball situation but it shouldn't happen either, not two matches in a row. It's just a case of taking out the video and seeing what went wrong."
