City, the first English club to play at the Olympic venue, surprised many by finishing ninth on their return to the top flight last year with a team largely made up of players that had won promotion from the Championship.
McLeish has added three players to his squad in the close season and is looking to make "one or two other additions" but believes the competitive nature of the league means it will be a hard feat to match this season.
"Expectation levels have risen in other peoples' minds but not in mine," the Scot told reporters.
"We are still developing as a club in the Premier League, we have young players who came from the Championship and they have to show they can do it all again.
"To finish ninth this season is a big, big ask because other teams will be spending a lot of money and those clubs who finished below us last year will want to get above Birmingham.
"Again Premier League survival is the biggest thing for us and then we can build again so we face a big, big challenge.
"You've got to spend three years in the Premier League and then people recognise you as a Premier League team."
O'CONNOR GOAL
A second half tap-in from substitute Garry O'Connor was enough to beat the Chinese champions on a hot and humid evening in the capital.
Watching in the stands alongside senior Communist Party officials was Carson Yeung, the Hong Kong tycoon who bought Birmingham last year.
McLeish said he would be delighted to bring Chinese players to St Andrews if he was given the wherewithal to identify the best young talent early enough to suit his budget.
"I'm hoping that Carson Yeung and the guys running the club can find me the scouts in China, Hong Kong and Asia to bring us the best young players before they go to Europe," he said.
"Because when they go to Europe it's too late for us as they cost too much money."
Both teams had complained about the pitch and McLeish said he was pleased they finished without any injuries.
The deserved victory was a second for Birmingham, after a win in Hong Kong, in their three-match tour which concludes in Shenyang at the weekend.
"We had a very poor pre-season last year, we lost a lot of games and then we had a fantastic season," said McLeish. "I hope this is not a bad omen having won these two games."
