Dyche was dismissed by Burnley on Friday after nearly ten years in charge of the club.
The 50-year-old was the longest serving manager in charge of a Premier League club, having been appointed in October 2012.
He led Burnley to two promotions to the Premier League, qualified for the Europa League in 2017/2018 season and only signed a new contract until the summer of 2025 last September.
Burnley find themselves in 18th position on the league table, having recorded just four wins all season and have only eight games to salvage their campaign.
Jackson will be in charge of the Clarets when they visit West Ham United on Sunday.
"I think it has come as a shock to the players," Jackson said ahead of the game.
"That is human nature, but they are an experienced group.
"For us it's about the whole club coming together - everyone here, the fans and everybody bunkering in to take away all the noise and concentrate on what we need to do."
"He can be unbelievably proud of what he has achieved here - two promotions, a European qualification."
"But I think more than anything else he has built not only a club, but a culture and identity. That is really difficult to do in football sometimes.
"It takes time and takes someone who knows what they are doing and what they want."
He added: "I briefly spoke to him. It's not easy, what do you say to someone who has lost his job, who has done so much for the club?
"I don't know what you say to him, being deadly honest. It is sad but we have to find a way to move on from that. What he has done for this club has been terrific."
