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 yesterday.
Point to prove: McLeish is hoping Cup success won't distract his players from their league duties
McLeish was able to give some of his key players a rare break against the Owls.
The Blues boss said: 'It is great to be involved in the cup competitions at this stage.
'But I hope it doesn't take its toll in terms of our premier goal, which is Premier League status.
'My big craving is the Premier League.
'We definitely don't want the cup runs to take the steam out of the players.'
Smart move: Martins (centre) celebrates after scoring his first goal for the Blues at St.Andrews
McLeish added: '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.
'That's why being able to recharge the batteries of a few of them this weekend was a Godsend.
'We left out a few players for next week's final which should benefit us.'
Hleb will have a scan in the next 24hours after being stretchered off against the Owls after setting up theopening two goals for Jean Beausejour and Obafemi Martins.
The fiery Scot revealed: 'He was limpingheavily 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.'
Spell on the sidelines: Hleb is stretchered after picking up an injury in the Blues FA Cup win
McLeish substituted key defender Roger Johnson midway through the second half, after he had been booked, to avoid a possible sending-off.
Johnson looked far from happy, banging his fists against the dug-out, and it needed first team coach Peter Grant to calm him down with a quiet word in his ear.
But McLeish insisted: 'I did the sensible thing when taking the big fellow (Johnson) off.
'It was right. He plays with passion and was a bit on fire at the time.
'He had got the booking and he is that eager to get in front of the strikers and beat them in the air, which he has done so well.
'I thought if he mistimed a tackle, he could get a second yellow card and that would be disastrous for us as a team (for the final).
'We need Roger. He has been a stalwart since he has come to this club.'
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.
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Explore more:People: Roger Johnson, David Murphy, Obafemi Martins, Alex McLeish Places: Birmingham, Newcastle