The Blues will contest the Carling Cup final next weekend and are also through to the quarter-finals of the FA Cup after disposing of Sheffield Wednesday 3-0 at St Andrew’s on Saturday.
McLeish was able to give some of his key players a rare break against the Owls but is worried a heavy schedule may have a telling effect on his small squad, reduced even further by Alexander Hleb’s suspected medial knee ligament injury.
McLeish said: “My big craving is the Premier League. We definitely don’t want the cup runs to take the steam out of the players.
“I know they have got enormous character but, when I look back at the last league game against Newcastle, we looked flat and short of inspiration.
“That is always the danger, that the longer the season goes, some minds become tired as well as the bodies. I think mental tiredness is the biggest concern.
He added: “We left out a few players for next week’s final which should benefit us.”
Hleb will have a scan today after being stretchered off against the Owls after setting up the opening two goals for Jean Beausejour and Obafemi Martins.
McLeish said: “He was limping heavily after the game. It doesn’t look good. It could be his medial ligament. We will see what the scan says but we are a bit concerned.”
Beausejour and Martins both scored their first goals for Birmingham before half-time and then David Murphy netted the third early in the second period to kill off the tie.