And McLeish knows Benitez will be aware history and his past achievements will count for nothing with his critics ahead of Monday's Barclays Premier League clash between the two clubs at Anfield.
The Reds are facing possible elimination from the Champions League after a 1-1 draw in Lyon last night with their destiny now out of their own hands.
McLeish said: "I think Rafa Benitez is a smart guy who has been in the game a long time and knows the expectation levels at a club like Liverpool, the same as I did at Rangers.
"We are not daft. When you have some results that are against expectations of the fans and what people expect of Liverpool, then you are always going to be under pressure.
"I was no different with the Rangers job but you have just got to keep your focus, your dignity and keep working as best as you know in the game."