Dyche undoubtedly arrived at Forest in difficult circumstances, but he appeared to steady the ship after a poor run of results under Postecoglou, winning seven of his first 12 games.
If results were taken from when Dyche took over, Forest would be mid-table, six points above third-from-bottom Tottenham.
“That’s the only thing I’m frustrated about as it’s not a terrible run,” added Dyche.
“But that’s still the modern way football is. Demand is high. That’s changed enormously in the last probably two years.
“Demand is getting higher and higher and higher and higher. Expectation immediately grows.”
Former Newcastle striker Alan Shearer believes Dyche should be given more time.
“I think with his know-how and his experience in the Premier League, I would without a doubt stick with Sean Dyche,” he said on BBC Match of the Day.
Ex-Liverpool midfielder Danny Murphy agreed.
“I think for this battle at the bottom you wouldn’t want a better manager than him,” he said.
“He’s been there, done it, he stays calm. I think they’d be crazy to get rid of him but it doesn’t mean it’s not going to happen.
“The other thing as well I suppose for Marinakis is if it wasn’t for him they wouldn’t be in the Premier League and they wouldn’t be in Europe so maybe he’s got the right to do what he wants, but I don’t think there’s a manager you could bring in who is as capable as him in this fight.”
Former Everton defender Phil Jagielka added on BBC Radio 5 Live: “Sean Dyche came in to do a job and that job was to make sure they stayed out of the relegation zone. He’s picked up a few points. It wasn’t too dissimilar to the job he had to do at Everton.
“We know that this owner doesn’t like watching his team underperform and he’s not scared to make big decisions.”