Skipper Andy Butler saw red for the Saddlers in just the 18th minute and David Mooney duly put the League One leaders ahead at the break.
"I thought we were outstanding on the ball and when we were without the ball we restricted them. They've been on such a fantastic run, winning eight games out of eight, that they don't really need a helping hand with the sending-off," Smith said. "I've seen the incident again on the DVD and I think it's a great tackle.
"We regrouped, Ben Purkiss did fantastically well when he went on, James Chambers was outstanding but, to a man, we were outstanding and I think that even the most loyal Leyton Orient fan would probably say we deserved a point.
"We've had a man sent off and then given them a goal, really, but our 'keeper (Richard O'Donnell) has made a couple of really important saves and done really well for us.
"In the end they had to resort to putting long balls into our box because we were so disciplined off the ball.
"At times we had to be really solid but when we had the ball I thought we used it really intelligently. I told the lads at half-time that chances would come and when one did, Craig Westcarr popped it in. So I'm really pleased with our performance and proud of our lads."