The Gunners conceded just before the break but, following their boss's fury, the England international scored the first of three second-half as the north Londoners put Champions League qualification in their own hands.
"We got a rocket at half-time," Walcott told reporters. "We'll keep that in the dressing room but it's great that the manager has that passion and it got a bit more out of the players. The manager gave us a kick up the backside.
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"We want to keep our form going. We haven't lost now in a long time; I have lost count. We just have great experience in knowing what to do when the time is right.
"It's funny, it happens every year - we tend to finish very strong. I think it is just because the players want Champions League football so much. We all know how big it is to be in the Champions League - not just for the manager but the fans, the players and the club itself. It's massive.
"We have been in it for the last 15 years and we don't want to be the [first Arsenal] players who are not part of that.
"It is a tough game and we cannot underestimate Newcastle. I know it was a totally crazy game when we played them [in December, a 7-3 win] but we are ready for it.
"We won't let a 4-0 lead slip if we get one this time! If we show the passion and commitment that we did in the second half [against Wigan], we will be OK."
Having netted a poacher's goal against the Latics, Walcott was again asked about his hopes to feature more as a centre forward.
"Wherever the manager wants to play me, I will do that for the team," he insisted. "It's well documented that I want to play there more but things are going well and I am enjoying my football.
"I am making runs in and the manager is playing me up front now and then. I can wander at times and it works - there is a lot of rotation in that front line so, when it is working, don't change it."