De Zerbi arrived with Tottenham fighting to avoid relegation last season and helped keep the club in the Premier League. He then challenged the owners to give him the squad needed to compete at a higher level.
Tottenham have responded by spending heavily, including major attacking additions from Manchester City.
"I didn't expect a transfer window like we have done," De Zerbi said ahead of Saturday's Premier League meeting with Newcastle United.
The Italian believes Tottenham could still make one more signing before the window closes, with discussions taking place between the manager, owners and senior figures at the club.
"I think we can do one player more in one specific position," he said.
"Yesterday we went to dinner with the owners, Johan, sporting director, and chief executive Vinai Venkatesham and we spoke about this.
"All of us are on the same page and a very good connection."
Brazilian winger Savinho, signed for 75 million pounds, made an immediate impact by scoring on his debut in Wednesday's 5-1 League Cup win over Charlton Athletic.
Egyptian forward Omar Marmoush has also arrived from Manchester City on loan, with Tottenham reportedly committed to a 50-million-pound permanent transfer next summer.
De Zerbi believes Marmoush can give Tottenham another attacking dimension.
"Great signing for us, great player. Another great player. Everyone of us love him as a player and we hope he can do what he is able to," he said.
"He can give us more solutions in attack. We need more players in attack capable of scoring goals.
"Very fast player. Works well. A very smart player. He thinks like a coach. He can play in different positions on the pitch."
De Zerbi was equally enthusiastic about the attacking options available to him, describing Savinho and Marmoush as "bomba" – stars capable of making a major impact.
The spending has not yet produced the perfect start, however. Tottenham were beaten 3-0 by Brentford on the opening weekend of the Premier League season.
De Zerbi accepts there is still work to do, but he remains pleased with the club's business.
Tottenham have also brought in midfielders Sandro Tonali and Mateus Fernandes, as well as defender Jan Paul van Hecke.
The club have reportedly been linked with Liverpool forward Cody Gakpo, although De Zerbi admits he dislikes the transfer window remaining open once the season has started.
"I think it's crazy but at the end we are very happy with the transfer market we have done until now," he said.
Tottenham now have an expensive squad to mould into a team capable of challenging at the top end of the Premier League.
Their next test comes against Newcastle United at Tottenham Hotspur Stadium on Saturday, when De Zerbi will get another chance to see whether his new-look side can turn their huge summer investment into results.
