The Azerbaijani champions were valiant 2-0 losers on their first trip to San Siro, the visitors only beaten after Mauro Icardi's sealer in the 85th minute on Thursday.
Mazzarri claimed there were no easy wins for his side, who have not been a top-four team in Serie A since the 2010-11 season but are still considered strong in the European second tier.
"With modern football all the games have levelled out," Mazzarri told Mediaset Premium.
"We must always try to win or it gets turned into a tragedy by the media.
"We are forced to get a result. Don't forget in this environment the only thing that counts is the result."
Mazzarri said Gary Medel's half-hour cameo in Milan was impressive, the Chilean defensive midfielder settling the hosts in the back half as they held onto their one-goal lead before Icardi's sealer.
The coach was also pleased with French midfielder Yann M'Vila's contribution.
"I liked M'Vila and Medel did very well, as when he came on the team became more solid and didn't suffer any more," Mazzarri added.
"Those two can play together from the start, but we have to work towards that gradually, as there are a series of mechanisms and tests to be worked out. It is a tempting idea, though."
Such has been Inter's fall from grace in the past three seasons, they have suffered terrible defeats - none worse than their 4-1 home loss to Cagliari on Sunday.
Mazzarri, though, praised his players and the home support for overseeing their immediate bounce back to winning ways.
"The lads played a difficult and focused game, which was not easy after losing 4-1 to Cagliari," the former Napoli tactician said.
"I really want to thank the fans in the Curva who were exceptional and supported the team throughout the game.
"This was our sixth game in a row for many players and that takes up an incredible amount of energy.
"We learned the lessons from the Cagliari defeat."
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