McLeish was speaking ahead of Sunday's FA Cup tie at the Emirates Stadium.
Wenger came in for strong criticism from Gunners fans after substituting Alex Oxlade-Chamberlain during the closing stages of last weekend's home clash with Manchester United.
Arsenal's 2-1 setback was also their third defeat in a row and they are facing a battle to secure a Champions League spot for next season.
But McLeish insists injuries, particularly in defensive areas, have taken their toll on the north London club.
When asked about the pressure on Wenger from Arsenal fans, McLeish said: "The name of the game is results and we are all governed by that in terms of the reaction of the fans.
"We can't complain. That is part of the game and you know if you don't get the results, you know you are going to get a bit of stick and criticism.
"Arsenal have had a good season up to two or three weeks ago but they have had a lot of injuries.
"They are missing great full-backs, also missing Mikel Arteta, and yet people expect them to still keep beating teams like Manchester United who are at full strength.
"They are still a great side, will definitely be favourites against us but we don't fear this game.
"We feel we've got a chance if we play to our capabilities."
McLeish was manager of Birmingham when they achieved a shock 2-1 victory over Arsenal in last season's Carling Cup final.
But he is unsure whether that triumphed marked the start of a slow decline for the Gunners or whether it affected them psychologically.
He said: "I don't know if that was the catalyst but we wanted to win the cup every bit as much as Arsenal did and we earned the right to do that.
"That is history but history will tell you also the Birmingham team struggled after that and again it was to do with a lot of injuries.
"No-one can continue to play at the top end of your game if most of your key men are out through injuries."
McLeish will be looking for another significant contribution from striker Robbie Keane and the on loan Los Angeles Galaxy player netted twice on his full debut at Wolves last weekend.
But he has ruled out the possibility of extending Keane's stay or trying to make it permanent.
He said: "Have we done anything about extending Keane's stay? No, his parent club is LA Galaxy and there is an agreement in place.
"We said if Robbie could come and give everyone a boost, get a couple of goals, make a significant difference in the other games, then great. But that's it."
Strikers Gabriel Agbonlahor (illness) and Emile Heskey (achilles) plus midfielder Stephen Ireland (hamstring) are all back in contention.
But winger Charles N'Zogbia is again ruled out with a heel problem.
