Borriello struck in Milan's thrilling 4-3 victory over Cagliari on Sunday.
Speaking to Milan's official website, Borriello said: "I am happy to have received praise from Galliani after this game.
"I was involved in all four goals, which means if my team-mates give me the chance to play I can always do better.
"It's not a criticism, but being a new team we have to find the right mechanisms and try new things. If in the future there is the right level of trust in each other, seeing that on Sunday things went well, then we could find ourselves in the same situations again.
"We suffer a lot on the pitch, but games like this give you great emotions. We have to manage the end of games better and we are working on this aspect.
"My goal was lucky. It was a very easy one to score. Pato did well and fortunately I found myself ready. We now have to think about working towards Marseille.
"My first objective is that of playing for the performance and not principally to score goals. What interests me is how the team feels to me.
"At the moment, I feel good, but I know that I always have to show something because I play in a team like Milan. I wear an important jersey that has been worn by players who have made history and for this reason every time I go on the pitch I have to give my spirit for this jersey."