The result means that Everton missed the chance to move above Merseyside rivals Liverpool into the top four, and Barry admits that his side had drawn too many games already this season.
"We knew it was going to be tough. They were going to go right to the end. At the end of the game I had a great chance from eight yards out - it's a shame [the West Brom defence] all pushed up," Barry told Sky Sports News.
"It was a fair result in the end. It's nine draws for us now and that's too many. But if we show the form that we showed at start of season then we'll be there or thereabouts."
Everton will have another chance to move above Liverpool when the two sides face each other in a Merseyside derby at Anfield next Tuesday.