That means Spurs have now failed to score in their opening three league games for the first time since 1974/75 with just one point picked up.
De Zerbi has spent heavily to bolster his squad over the summer including a club record £100M transfer deal for fellow Italian Sandro Tonali.
Tonali, Jan Paul Van Hecke, Savio, Mathys Tel and Omar Marmoush were among the new signings who started at Forest, and De Zerbi dismissed claims of a panic in his squad.
"We've bought very, very good players, but you can't just build the team with names like in Football Manager.
"We're disappointed for the result, but for the performance, I'm very happy. Considering we started to work together last Thursday for the first time, for the first day.
"We have to improve in every part of football, organisation with and without the ball. I thought we defended very well.
"We have to work because I think we played very well with the ball, we found solutions. I think we can be much better in the final third."