Spurs rescued a 1-1 draw at Old Trafford on Saturday, with Dominic Solanke scoring a late equaliser after Rodrigo Bentancur had been sent off.
Tottenham impressed for long periods in the first half but fell behind when Bryan Mbeumo scored in the 73rd minute. Bentancur's red card five minutes later made their task even harder, but De Zerbi's players refused to give up.
Solanke, wearing the captain's armband for the first time, secured a point with a glancing header in the 92nd minute. It was also his first goal of the season.
De Zerbi believes the result demonstrated the togetherness he wants to see more consistently from his squad. The Italian sees Tottenham's nine-day break before their next fixture as an important opportunity to build on that performance during a training camp in Marbella, Spain.
"We have to build the team," De Zerbi said.
"Now the target is to build the team, not the group of the players. We are a great group of players, but we are not a team yet."
The head coach was encouraged by the way his players responded to adversity against United, particularly after going down to 10 men.
"This game (Manchester United), we show to be a team. To be a team is to play for the team-mates, suffer together, attack together, defend together," he said.
De Zerbi also stressed that players introduced late in matches must be ready to make an immediate contribution, rather than seeing themselves as substitutes with a lesser role.
"The players who come inside five minutes, three minutes, like Mateus Fernandes, they have to play like they are in the first 11, without problems, without other faults," he added.
The Italian wants his squad to combine confidence with the hunger to improve, both on the training ground and during matches.
"We have to find the balance between the confidence in ourselves and to be hungry in the training and in the games."
Tottenham will hope the work in Spain helps them develop greater consistency and a stronger collective identity before returning to action against Coventry City on Monday at the Tottenham Hotspur Stadium.
Morgan Rogers has credited Xabi Alonso's team talks for Chelsea's impressive starts to matches this season after the Blues raced to a 5-1 victory over Bournemouth at Stamford Bridge.
Manuel Akanji has admitted he is unsure what will happen to Manchester City's trophies following the club's guilty verdict over financial rule breaches, but the Inter Milan defender hopes he will get to keep his titles.
Michael Carrick has praised Mikel Arteta for building a successful team at Arsenal but admitted that the Spaniard's achievements are difficult to celebrate because of Manchester United's historic rivalry with the Gunners.
Coventry City produced a superb performance to beat Newcastle United 4-1 at the Coventry Building Society Arena, securing their first home Premier League victory in 25 years and climbing out of the relegation zone.
