If Inter were looking for a confidence boost before next weekend's crucial derby meeting with AC Milan then they were sorely disappointed as La Viola dominated from start to finish, with Adem Ljajic and Stevan Jovetic grabbing two goals each at the Stadio Artemio Franchi.
Antonio Cassano did go on to score the best goal of the game but his sour-faced refusal to celebrate was indicative of how downhearted the visiting team felt at the final whistle.
Inter must visit Romania for the second leg of a Europa League tie with Cluj before turning their attentions to the second Derby della Madonnina of the season, and Stramaccioni admits he failed to rotate his squad properly for last night's game.
He told inter.it: "I think it's clear what happened today. Regardless of the merits of our opponents, I think we paid for the Europa League match in midweek.
"Probably I myself hadn't imagined what would happen after having played two games with the same players. And, while being able to foresee it, I never imagined we would have paid so dearly.
"This Inter was too ugly to be true, but I think it's possible to have a heavy defeat like this in the league.
"It's certainly not something we needed, but you can't have a Thursday like the last one we had, then something like this."
With his thoughts turning to the derby and dislodging the Rossoneri from third place, Stramaccioni is eager to regain the trust of the Inter fans.
He added: "We absolutely have to recover, but I'll say again that other teams this season have suffered heavy losses, and it's all about how you react to them.
"Again, it's not a coincidence that another defeat came after a Europa League match."