Nigel de Jong's second-half header was the only goal of a drab Derby della Madonnina as Clarence Seedorf's side took city bragging rights and a step closer to securing a Europa League place.
And Mazzarri had little excuse for a lacklustre performance, as his players failed to match their usual level of intensity.
"We weren't ourselves, the tension got to us," Mazzarri said after watching his team fail to register a shot on target.
"We didn't play well, as everyone saw. We did better in the first half, but cared so much about this game that we used up a lot of nervous energy beforehand."
Despite the result, Mazzarri urged Inter to finish the season strongly and secure their own spot in next year's Europa League.
"Unfortunately, this season has been up and down. Milan were more vehement in the tackle and first to the ball, so they won.
"Now we have to try and get as high up the table as possible; the situation is still in our hands and we've got to play better than this."