Spurs' 2-1 defeat at home to Southampton means north London rivals Arsenal could still pip them to second.
"I don't care about Arsenal," said Pochettino. "Sure I want to be above them, but this is normal.
"We need to concentrate on us and not what is happening with our neighbours."
Having seen their bid for a first title since 1961 ended by Monday's 2-2 draw with Chelsea, Tottenham have now not won in three games and have only two victories in their past six.
The results mean Spurs remain in second, two points above Arsenal, and travel to Newcastle on Sunday for the final game of the season. The Gunners host already relegated Aston Villa at the same time.
But the Argentine said his players had not been affected by Monday's disappointment in the defeat by Saints.
"We did not lose the game today because of last Monday's result," Pochettino told BBC Sport. "We lost because we conceded two goals.
"We feel very disappointed, losing our last home game of the season. But we are still in a great position."