The England international returned to Premier League action on Saturday afternoon after a disappointing fortnight of international football for the 27-year-old forward.
Walcott had scored three times and made two assists in seven Premier League games ahead of the international break after the forward hit the ground running.
And Arsenal’s longest-serving player scored twice in the first half of the north London side’s 3-2 win against Swansea City at the Emirates Stadium to take his tally to five goals for the top-flight campaign so far.
Walcott missed two chances in the second half to complete his hat-trick and quash the possibility of a late Swansea equaliser.
But former Arsenal striker Wright refused to criticise the England star for his wastefulness in the second half before he backed Walcott to produce goals when it really matters.
“He scored two really good goals,” Wright told BT Sport.
“Yes – you’d want him to be more ruthless and finish those other chances as well and make it even more comfortable. You have to take what you get.”
Wright added: “We are getting more this season. He has equalled his tally with five goals.
“As his confidence grows and he continues to score, he will score more important goals because he is in a rich vein of goal-scoring at the minute.”
Arsenal are level on points with Premier League leaders Manchester City following their 3-2 win against Swansea City.
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