Arsenal saw off Tottenham to grab the final Champions League place.
Walcott admitted: "It was so tense. Newcastle showed they shouldn't be where they are in the league.
"They were fantastic. We had to dig deep.
"We didn't know the Tottenham score. They did their job.
"We knew it was in our hands and had to do our job. I'd like to say it is a shame but it's not."