The on-loan from Manchester City stopper made a number of superb saves against the Premier League leaders at St Andrews on Boxing Day.
"Joe has come on a ton, we talked about one or two things earlier in the season and he has improved," McLeish told Sky Sports.
"I'm pleased for him because he is a conscientious guy, he's his own biggest critic and he wants to get better and better.
"Chelsea had their moments. We had one or two issues, we had a little bit of luck and we put in some fantastic defending.
"But Chelsea have so much quality it won't be long before they start winning again. They will roll up their sleeves I'm sure."