Blues took a 17th-minute lead through Jean Beausejour's header but John Heitinga rifled in an equaliser 10 minutes before the interval and the Toffees looked by far the more likely side to find a winner in the second half. However, Blues held on for the 1-1 draw, taking them up to 17th in the table, with West Ham dropping into the bottom three.
"I think that an apt way to describe it is - a battling point," McLeish said.
"We started very brightly and got the opening goal. Then the players showed that tremendous resilience that they have."
He added: "We tried to be a little bit more predatory, but we never really had the composure in terms of the passing in the second half.
"But sometimes you need to get points in an ugly fashion."