A brace from Mauro Icardi and further goals from Walter Samuel and Rodrigo Palacio ensured Inter moved back into the top five after Parma's 1-1 draw at Bologna.
Inter are now two points clear of Parma in fifth - which comes with the final UEFA Europa League spot - but rode their luck during the first half at the Stadio Comunale Luigi Ferraris, as Handanovic saved Maxi Lopez's penalty before Eder was dismissed for the hosts.
Inter made the most of their chances after the break and the Slovenian goalkeeper claims the points from their victory are all that matter.
"The important thing for me was winning. However, it wasn't a positive day since the game could have turned out differently, honestly speaking," he said.
"We need to start thinking now about Parma and Europe.
"Europe is neither nearer nor further away. There are three or four teams fighting for those spots.
"I'll be happy when we're competing for something more important."
