Walcott was just offside when he received Tomas Rosicky's pass to open the scoring after two minutes.
The England striker said: "I play to the whistle. People have said I'm offside but it's not my problem, I just need to finish it.
"It's been a while, so I'm happy with the goal but I would have preferred a win.
"It will feel like a loss but we have to keep our heads up, there are three very important games still to play."