Nicolo Zaniolo returned to action for the first time since January as Roma lost at Napoli on Sunday.
Inter boss Antonio Conte could scarcely disguise his anger after his side were beaten by Bologna before Atalanta applied further pressure.
Inter have doubled down on their desire to keep hold of Lautaro Martinez, who continues to be linked with Barcelona.
Bologna scored twice inside the final 16 minutes to seal all three points against Inter, who had taken the lead through Romelu Lukaku.
Juventus defender Matthijs de Ligt took time to get going after arriving from Ajax and has admitted he struggled with the criticism.
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