Arsene Wengerâ€™s side were forced to dig deep for the three points following Carl Jenkinsonâ€™s red card, and Walcott was delighted they showed their battling qualities.
â€śIt was an important win,â€ť the England international told arsenal.com. â€śThe three points have us on a high and weâ€™ve got a nice week now without any midweek game.
â€śA lot of players are back from international duty and need a bit of a break. Some may be rested for the FA Cup game, but thatâ€™s just as important as we want to go far in that competition. If we lost [at Sunderland], we would have been dwelling on it for so long, so Iâ€™m glad we didnâ€™t.
â€śWeâ€™re very confident [of finishing in the top four]. We can battle through any sort of situation. The teams around us are winning as well, but weâ€™ve just got to make sure we look after ourselves and try to win as often as we can.
â€śWeâ€™ll see where we are at the end of the season but weâ€™ve got to show the belief we did at Sunderland. I felt there were a lot of winners in that dressing room and the boys were fantastic.â€ť