The forward has only scored four goals since arriving at St Andrew's last summer and McLeish added: "He was difficult to play at times. He stood his ground, used all his assets and held the ball well at times. It has been a difficult first few months for him in England."
Birmingham, who play Arsenal in their first major Wembley final in 55 years on 27 February, were second best in the first half and their task was made more difficult when Carlton Cole scored with an exquisite strike from outside the area.
But second-half goals from Lee Bowyer and Roger Johnson, which involved Zigic in the build-up, ensured extra time before Gardner scored with a sweet angled strike, having twice hit the post with efforts earlier on.
And McLeish was quick to praise the efforts of his senior players, telling BBC Radio 5 live: "Credit goes to the players because they carried it out in the second half. Sometimes players don't have the bottle, but mine did.
"In the second-half Barry Ferguson, Lee Bowyer and Steven Carr's experience came to the fore and they were vital and we had a cracker [of a goal] from Bowyer."
McLeish, who won five cups with Rangers as a manager, said he was excited about next month's final at Wembley but would not be overawed by playing Arsenal.
"I haven't been fortunate to lead a team out at Wembley before," he said.
It's a huge disappointment but we will pick out the positives
West Ham boss Avram Grant
"It fills me with pride. I've got to finals in Scotland but to come to England and get to Wembley is a dream come true.
"They've got so many classy players but it's 11 v 11 and you've got to believe you've got a chance.
"We don't want to attempt to mirror the way Arsenal play because we don't have that quality but we have seen teams like Martin O'Neill's Leicester winning [the Carling Cup] before and that's what we have to take inspiration from."
Meanwhile, West Ham boss Avram Grant was almost at a loss to explain how his side managed to lose.
"Everything was going well. We were playing well and scored a goal," said Israeli Grant, who position has been under scrutiny in the past two months.
"I didn't know what to say to them at half-time. But then Birmingham put pressure on the team and we didn't deal well with the two corners that led to their first two goals.
"It's a huge disappointment but we will pick out the positives because tonight the team showed they can play good football."
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