The Gunners headed into the clash seeking their 10th straight win in all competitions following their opening-day defeat by Aston Villa at Emirates Stadium.
But Jack Wilshere’s goal earned the north Londoners a point after Claudio Yacob had given Steve Clarke’s men a first-half lead at The Hawthorns.
“I suppose when we come down a little bit we’ll be happy with that point,” Szczesny told Arsenal Player.
“I was disappointed after the game because we felt confident, we had the momentum. It was a tough game so we’ll probably take it. But I’m still disappointed.”
Arsenal, who next host Norwich City, moved back to the top of the Premier League table thanks to the draw, overtaking Liverpool on goals scored.
And goalkeeper Szczesny has called on the Gunners to string together a fresh run of positive results when they return to action after the international break.
“It’s time for us to start a new run,” he said. “Hopefully we can win the next game and the few more after that, and create the momentum again. We’re still top of the league so the momentum is still with us. We won’t lose our confidence.
“We said to ourselves before the game that we want to go into the break top of the league. Obviously we would have preferred to have done it with a win but we got a point which was enough to keep us on top.”
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