City were considered by many pundits to be one of the favourites for promotion before the season started and 2-1 victories over Sheffield United and Colchester United to start the term have justified those assertions.
Next up is a potentially tricky encounter with last season's play-off runners-up Leyton Orient at Ashton Gate on Tuesday.
And Cotterill is keen for his squad to remain grounded.
"It's a decent start, but no more than that," he said after defeating Colchester on Saturday. "We can be fitter and sharper in our thinking.
"We have a new pitch, which is a bit quicker than the players have been used to and it will take time to adjust. But I'm pleased with the effort of the players and feel I have a really good group."
Part of City's early success has been down to close-season signing Aaron Wilbraham, the striker has three league goals to his name already and Cotterill has urged the 34-year-old to continue being selfish in front of goal.
He added: "Aaron has been more known as a goal-maker during his career, but I have told him to think of himself more and grab a bit more glory."
Sheffield United were another much-fancied side ahead of the campaign, but Nigel Clough's men have started with back-to-back league defeats.
The South Yorkshire team travel to London Road on Tuesday to meet a Peterborough United side buoyed by taking maximum points, and with manager Darren Ferguson confirming bids have been made for four new players they could soon become even stronger.
"We are trying to do business the right way and get the right players in - and we will almost certainly have something done on Monday," said Ferguson after Saturday's 3-2 win over MK Dons.
Last season's League Two champions, Chesterfield, have also taken six points thus far, along with Crawley Town, and the duo have home matches with MK Dons and Bradford City respectively.
Scunthorpe United and Fleetwood Town meet at Glanford Park in a match that pits two promoted sides against one another.
They have had contrasting fortunes so far, with Scunthorpe taking no points and conceding seven goals, while Fleetwood have earned maximum points after wins over Crewe Alexandra and Notts County.
Crewe and Rochdale are both pointless but that will soon change when they meet at Gresty Road, while Yeovil Town look for their first points of the campaign at Walsall.
Other matches see Coventry City tackle Barnsley, Doncaster Rovers host Preston North End, Gillingham welcome Swindon Town and Colchester and Port Vale take to the road to face Notts County and Oldham Athletic respectively.
