Spalletti saw his side fall behind to a 23rd-minute Lucho Gonzalez header at the Petrovsky Stadium, with a Hulk goal five minutes later restoring parity.
The hosts could have won the game were it not for a saved Hulk penalty seven minutes after the break, but Spalletti believes his side must start games in a more positive fashion if they are to qualify for the knockout stage.
Zenit currently sit second in Group G, one point above Porto with two matches remaining.
"It is difficult to explain why we start badly in the UEFA Champions League," said Spalletti.
"It's not the first time we are in such a situation. In the first half Porto were the better team; maybe they were stronger than us physically.
"By the end of the half we managed to find our game, and after the break we took the initiative. I can't even describe how well my lads played in the second half.
"We must remain calm and try to achieve a result in the next two matches in the Champions League."
Spalletti also refused to lay any blame at Hulk's door for the failed spot-kick against his former club.
"It is always better to leave the choice of penalty taker at the mercy of the players, as we always do," he continued.
"The only situation where a coach can intervene is when players can not solve their own choice.
"In the second half, everyone could see that we can play at such a high level. And this level, we can show in the game against Atletico."
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