Blues are just three points above the bottom three after a poor recent run of results. But at St Andrew's the Carling Cup holders have collected seven points from the last nine via wins over Bolton and Sunderland and a draw against Wolves with 10 men.
McLeish said: "We've had three hard away games at Chelsea, Liverpool and Newcastle in the last four matches.
"We haven't done enough to get past 40 points but we've had terrific results in the last three home games that have got us to 39.
"Our form at St Andrew's of late has been good and I would back us against anyone in front of our own fans.
"Yes, we need a result against Fulham. They are a hard team to play against, have good movement, are a good footballing side. They have some fantastic forwards.
"It will be a tough game for us but we are at St Andrew's, we have got that magic crowd behind us and they can give us that extra couple of per cent.
"The battle goes on and we have to keep fighting to the last. We have to make that final push and that's what we will be endeavouring to do."
Source: PA
Source: PA