The 52-year-old was pleased with the Serie A outfit's display and singled out Hernanes and Mateo Kovacic for special praise
Mauro Icardi gifted the Serie A outfit the lead shortly before the interval, with Dod and Danilo D'Ambrosio effectively putting the tie to bed in the second half.
"It was good that we managed to break the deadlock," Mazzarri told Inter Channel.
"It wasn't easy at the start because they got men behind the ball and battened down the hatches, waiting to strike on the counter. We were smart enough to bide our time and wait for the goal to come.
"Getting the second straight after the restart was important too, and it came following a nicely worked move. Up until that point we were very careful in making sure we weren't caught on the counterattack.
"Maybe we started to wane a bit physically towards the end and we ended up letting them in a few times."
Mazzarri also spoke highly of midfielders Hernanes and Mateo Kovacic, stressing the pair were finding their feet as Inter generals.
"Hernanes did pretty well. He's improving, as all the players are. He and Mateo played well tonight, because they had to work hard and both defend and attack.
"I've mentioned those two but overall I'm happy with how all the lads played."
The return will take place at the Giuseppe Meazza on August 28.