I think this is normal because the Premier League is more important for them. If they are in the relegation zone next year in the Premier League, it will be a big problem for them. The Europa League is an important trophy and also gave them a ticket to the Champions League next year, but of course for the management, the ranking they are in this year in the league was more than enough for the manager to be dismissed from the team, in my opinion.
Don't forget Postecoglou took over Tottenham during 2023/2024 season, he brought the team to finish 5th and they did not win any trophy that season, he gave the assurance that he starts winning from the second season of his carrier, which he did as said, despite the team finishing in a challenging spot in the Premier League, but it was only there the mess up happened, considering he won them Europa and that means they have to play in the Champions League next season, what he did for the club is enough for the management to overlook where they ended in the Premier League and give him another chance to coach the team.
Most Tottenham fans would certainly hope that the club will keep Ange Postecoglou, the Europa League trophy presented can at least erase the mistakes made in the Premier League. However, the management and the club top brass see the situation differently, and perhaps they think that with a different manager, Tottenham can rise and perform more consistently next season. Thomas Frank is reportedly close to joining Tottenham, and it seems that a deal will be done soon. In the meantime, I hope Ange Postecoglou finds a new club in the future, who treats him better. Overall, Tottenham will have to work twice as hard to be able to perform consistently, the pressure of the Champions League is very different from the Europa League.