The Londoner were defeated 3-1 at home by Crystal Palace with stand-in captain Micky van de Ven sent off shortly after Dominic Solanke had given Tottenham the lead.
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The loss leaves Spurs just one point above the relegation zone with nine games remaining. Tudor was asked if he believed the club hierarchy would let him continue, but he gave no clear answer.
"I don't think in their direction, I have my job to do and that's all," he told media.
"Maybe it will sound strange but I believe more after this game than I believed before. I saw something.
"I need to choose the right guys because the boat is going in the direction that I want to go and needs to go and who is in the boat can stay.”