Ten Hag was sacked by United on Monday after a string of poor results left the team in 14th place.
Speaking ahead of Everton's clash with Southampton, Dyche was asked about another manager losing his job.
Dyche said: "Firstly nobody wants to see managers get the sack but eventually that's the nature of the business and we all understand it.
"Results hadn't gone to their liking and Manchester United have a high demand. The only thing I would say is that there has been a fair time scale and resources available for such a highly regarded manager to get a grip on what it is.
"It's hard though, it's hard at any level. You've got to win games and eventually that's what you get judged on but I wish him well - I'm sure there will be something else big for him."