The head coach felt his side unhappily lost 1-0 to Tottenham on Saturday.
But he was again pleased with much of their performance after drawing 3-3 at Liverpool on his debut.
Albion had slipped to sixth place on Saturday night ahead of Manchester United’s game at Everton last night – still a staggering height. De Zerbi said: “I don’t know if we can stay there or not.
“I know we need to raise the bar.
“I’m not afraid to aim high.
“I’m not worried about getting it or not.
“I’m more worried about not setting the target very low because we’re worried we won’t be able to compete with the top six teams.”
De Zerbi received a warm welcome from the Amex and fans in the North Stand showed a picture of the boss on a large Italian flag.
He said: “I’m happy about that and I want to say thank you to the fans.
“I hope to bring them satisfaction.
“I hope that I can meet their expectations.”
https://www.theargus.co.uk/sport/23034924.roberto-de-zerbi-sends-message-brighton-fans/?ref=rss Roberto De Zerbi sends message to Brighton fans