"The position in the table is a concern for me, but I am not worried about myself," said Amorim, who has only managed to win four out of 14 Premier League games since assuming control in November.
"I hate to lose. That feeling is the worst. The rest I am not thinking about.
"I understand my situation, my job, I am confident in my work and I just want to win games."
Tottenham's first home league win since November came amid a spirit of revolt among their support.
Before kick-off and after the match Spurs fans again vented their frustration towards owners ENIC and chairman Daniel Levy.
A huge banner read "24 years, 16 managers, 1 trophy - Time for change" as a sizeable contingent of the home crowd joined a protest calling for Levy to go.
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However, the mood for Postecoglou was lifted even before kick-off as he was able to welcome back a host of first-team regulars who have been sidelined by injury.
'Quality players' return
Goalkeeper Guglielmo Vicario made his first appearance since November. Maddison returned to the starting line-up, while Destiny Udogie, Brennan Johnson and Wilson Odobert were on the bench.
"They are quality players. We've had it pretty tough the last two-and-a-half months," said Postecoglou. "It was important for us to win and gain some traction.
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"I certainly feel there is still a massive opportunity for us in this back half of the season and hopefully today is the start of that."
United have their own injury troubles with Amad Diallo joining Lisandro Martinez on the sidelines for the rest of the season and Kobbie Mainoo ruled out for a month.
Amorim had to name eight teenagers among his nine substitutes, forcing Rasmus Hojlund and Joshua Zirkzee to start together up front after both were overlooked for United's last league game - a 2-0 defeat to Crystal Palace.
Hojlund had the first chance when he fired too close to Vicario before the Italian flew to his left to deny Alejandro Garnacho.
Instead, Spurs got the opener when Andre Onana could only parry Lucas Bergvall's shot into the path of Maddison, who tapped into an empty net for his 10th goal of the season.
United should have been at least level by half-time as Garnacho blazed over a glorious opportunity with just Vicario to beat after being picked out by Bruno Fernandes.
Vicario continued to frustrate Garnacho with another fine save after the break.
Zirkzee wasted a huge chance to equalise 20 minutes from time when the Dutch international headed Noussair Mazraoui's cross wide with the goal gaping.
But United's inability to put the ball in the net comes as little surprise.
Only the bottom three plus Everton have scored fewer than United's 28 goals in 25 league games this season.
At the other end, Onana kept the visitors in the game by parrying Dejan Kulusevski's powerful effort.
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But even Spurs' makeshift backline could not be breached by Amorim's men to allow Postecoglou to see some light at the end of the tunnel.
(This story has not been edited by staff and is auto-generated from a syndicated feed.)