A deflected Fabian Ruiz strike was the only goal at San Siro on Wednesday night.
“When I say we have to cover the ball, play better in the two phases of attacking and defending, this is what I mean," Gattuso told Rai Sport.
“When you play against a strong team like Inter, you must respect them and give something more. I congratulate my lads, but I always want to see this attitude, as there are 17 games to go. We must respect every opponent and play with the concepts we practice during the week."
The second leg will be at the Stadio San Paolo on March 5.
“Inter are a strong team, who combine physical strength with technique. Naturally, we had to neutralise their strikers, because so much of the play goes through them.
“We passed it well in the first half and could've attacked with more determination, while we made a lot of mistakes after the break and Inter were pressing with vehemence.
“In my view, we need to improve how we play when off the ball, because that is where we tend to lose games. We also cannot underestimate anyone, as we conceded against Lecce with eight or nine men behind the ball, just standing there and hoping a teammate would fix it.
“I get the feeling with our team that the moment someone gets past the first press, they will go clear in our half. It's the first time in six-seven years of my coaching career that I've felt this.
“We've got to keep working, because we've done nothing yet."