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Spurs head to Carrow Road on Sunday two points clear of their north London rivals in fourth place.
With their superior goal difference, a point would be enough for Antonio Conte’s men to secure safe passage into the elite club competition once again and consign the Gunners to the Europa League.
Arsenal, though, could capitalise on any slip-up from Spurs at Carrow Road, where Norwich have won just three league games all season.
Smith, however, is fully focused on his team signing off with a decent performance in front of their own fans - which have been few and far between over a miserable campaign.
"I have had texts off Arsenal fans and I have had texts off Tottenham fans, but I have no allegiance to either so there is no extra motivation at all," the Norwich boss said.
"That (top four battle) doesn’t affect us at all. It is a game of football.
"It is our last home game of the season and last Premier League game of the season."
Smith told a press conference: "We will try and win the football game because we want to get the points, but there is no extra motivation (because we can deny Spurs a Champions League spot)."
Additional reporting from PA