The Blues lost 2-0 at Upton Park, following goals by Alessandro Diamanti and Carlton Cole.
McLeish told Sky Sports: “First-half I thought was fine, I didn’t feel that we were under any real threat.
“They made a push of sorts West Ham and I felt that the best chance was a set piece for them and we were undone a minute before half-time which is not like us.
“I saw the board go up and said ‘look lads, got to see it through to half-time’ and we gave the ball away.
“(Scott) Parker runs at our defence and gets the free-kick and that’s un-saveable that free-kick.”
He concluded: “First-half I wasn’t concerned at all until the Diamanti goal, but we’re still very much in it and if we can get something back but I don’t think we played as well second-half as we did first.”