Younes Kaboul headed home for Spurs in the 68th minute, but the hosts -- who started with unsettled Chelsea target Luka Modric -- conceded a fifth when Dzeko curled into the top corner in stoppage time and Harry Redknapp's side sit bottom of the table after losing their opening two league games.
"We played a really good game against what is a fantastic team," Mancini said. "I was always sure Dzeko would score a lot of goals for us, he always scored in Wolfsburg."
"This is a very long season and it's important that we started well. The next games will be very hard because now everyone thinks we will score three or four goals, but that is impossible."
Elsewhere on Sunday, Newcastle striker Leon Best bagged a clinical double to fire his side to a 2-1 victory over Fulham at St James' Park.
Clint Dempsey got one back for Fulham late on but, three games into Martin Jol's reign, the west London outfit have only one point.
Stoke''s Ryan Shotton scored in the closing moments as the FA Cup finalists snatched a dramatic 1-0 victory against West Brom at the Hawthorns on Sunday.
Shotton netted in the 89th minute after a mix-up between goalkeeper Ben Foster and centre-back Gabriel Tamas to condemn Albion to their third successive Premier League defeat and give Tony Pulis''s undefeated side their first league win of the season.
PTI