Pedro scored his first career treble to earn the Seagulls a 5-2 win at Sheffield United, with Facundo Buonanotte’s brilliant goal and Danny Welbeck’s late effort supplementing an impressive performance at Bramall Lane.
The Brazilian striker, a £30million summer signing from Watford, took his tally to 18 for the season in all competitions but De Zerbi wants more.
“I consider Joao Pedro a big potential player and my expectations for Joao are bigger than he is showing,” the Italian said.
“He is playing very well and he is scoring a lot of goals but I think he can reach another higher level and I push for it because I am working for Brighton but I am working for my players to improve them and for them to be better.”
Brighton made the semi-finals of this competition last season and are dreaming of another run, but have a gruelling schedule coming up with midweek Premier League and cup games before their Europa League campaign resumes.
“We try to play every competition in the best way,” he said. “I don’t know the future, in my head there is only one thing, the Luton game on Tuesday evening.
“We have to think game-by-game and competition-by-competition.”
The Blades rallied from 2-0 down in the first half to draw level thanks to goals from Gus Hamer and Will Osula, but they were outplayed at Bramall Lane.
They were also beaten semi-finalists in last season’s competition but can now focus on their relegation battle in the Premier League, which starts with a midweek trip to Crystal Palace.
Boss Chris Wilder said: “You don’t say it before but when the draw comes out it is a real difficult one to deal with, especially at home with the way they play.
“If we’d have limited them in terms of the decisions we made defensively and made better decisions at the top end of the pitch and had more quality it might have been a tighter game and we could have got a result.
“You just get punished, you can’t give away two penalties at home and try and win a game of football. I am quite happy in the terms of how we played.”