Spalletti's intense smile bordered on a grimace as he met Mazzarri with an almost aggressive handshake, captured by television cameras, as his opposite number appeared keen to end the exchange as quickly as possible.
But the Inter boss says his strange behaviour was all down to etiquette.
"I went to greet him, he did not seem to want to shake hands," Spalletti told Sky Sport Italia.
"When he shakes your hand, it’s always with a little timidity, even after he's won a game.
"I complimented him, he only offered the tip of his hand, so I squeezed it even harder.
"He won, he can be happy. He does not have to be afraid."
Inter missed the opportunity to move into third in Serie A thanks to an Adem Ljajic strike at the Stadio Olimpico, in a match that saw the Nerazzurri squander several goalscoring opportunities.
"There are times in football when things do not go the way you would like," Spalletti added.
"But we had less skill and clean passing in possession and allowed them too many counter-attacks, which sapped our energy.
"We needed to manage and control the game better, stifling their attacks.
"When things are not going well, sometimes you cannot force a result."