The Tigers have struggled on their return to the Championship, winning just four of 15 games to sit a lowly 18th in the table.
With Slutsky appointed in the hope he could lead a promotion challenge, the pressure is starting to mount on the Russian. However, he insists the Allam family are understanding of City’s predicament.
“I don’t have pressure form the owner,” he said. “We have very normal relationship and he support me. Of course, I understand the result is the best answer from the coach to supporters and everyone.
“But I have said before that, for me, outside pressure is nothing. The most pressure comes from me.”
Pressed on what had been said by the powers-that-be at the KCOM Stadium following back-to-back home defeats, Slutsky said: “He support me, he understands the situation and he told me I have the time to change the situation.
“I don’t have pressure from the owner. I didn’t ask him about time, he support me. Anyway, I can’t think about how much time I have. I am focused on the game against Sheffield (United).”
Slutsky cut a disconsolate figure in the wake of Tuesday’s 3-1 loss at home to Middlesbrough on a night when individual errors again proved costly.
“I try to keep a positive mood, of course, but this is very difficult because after each match I ask myself a lot of questions,” he said. “A coach doesn’t have an easy time in his career.
“Each club has a problem, an expectation. For me, we have problem because I didn’t have pre-season time with 50 per cent of the squad. I try and change the situation and work very hard and I hope results come back quickly.”