Mazzarri's men – who have lost just one Serie A fixture in the current campaign – took the lead in the 18th minute thanks to Fredy Guarin's far-post effort.
Guarin hit the post in the second half, while Eder also a goal disallowed for offside at the other end.
Inter missed a chance to go third in the Serie A table and Mazzarri was disappointed with his side's effort.
"In terms of the way I see football, it's the worst game my team has played this season," he said.
"We've always taken the game to our opponents, attacked them, like at Bologna for example. Today though we were a bit off-colour.
"Samp played very well against us and deserved a draw. We had a number of chances, we just needed to be meaner and more clinical, more experienced, just come up with some extra to put the game to bed.
"I didn't like the intensity we showed both with and without the ball.
"Obviously well done to Samp, but today's match was the worst we've played since I've been in charge, at least in terms of our football. A draw is a fair result."
The former Samp boss added: "It's just a shame we couldn't give him a win, it would have been great it to the new president and also good in terms of the league table, because we've dropped two more points after those we let slip against Torino, Bologna and Cagliari.
"Anyway, the president clapped us at the end. That's a great sign. But it hurts more to throw away points like this.
"We hope the president stays cool and calm as he is now. Then, of course, to have a good league season you need investment and good organisation."
