After the Clarets came from behind to win 2-1 at Vicarage Road on Saturday, with two late goals from Jack Cork and Josh Brownhill, former Manchester United skipper Keane said on Sky Sports that: "I don't mind the manager celebrating, but when I see everyone hugging and kissing, I think it's slightly over the top.”
Keane added that he feels his former Nottingham Forest teammate Sean Dyche would have got the same results Jackson has, in claiming 10 points from 12 in interim charge: "I know it's a big result, but they should have been doing it all season. I think Dyche would have got the same results, I really do.
"Listen, the decision has been made and it's been a good reaction."
Jackson responded to the comments: "When you win a game that late on, when everyone knows what's at stake, there's a lot of emotion.
"I didn't even think about it. Someone sent me it and told me what had been said, and I watched the clip back just to see, and I saw Josh go to the crowd at the end, all the lads in the middle, with each other - which we've encouraged - and we went to the away end and clapped the supporters.
"For as long as I know, that's what you usually do at a football match if you win, and your fans are still there.
"So I don't think it was an over-celebration.
"As soon as I saw it, my first thought was him (Roy Hodgson) because of what it meant to their team as well, so I don't think it was disrespectful, anything we've done, it's just emotion.
"These fans haven't been in stadiums for two years, and we've not had that sort of moment with them for a while, so I think you've got to enjoy those moments, but I don't think it was over the top.
"It's all about those moments, that's why you play the game, otherwise you'd just play in empty stadiums.
"Put the fans in, and it becomes a different animal, that's why you play, for the competitiveness, the enjoyment, and that.”
The crowd have really bought into what the team are trying to achieve, with a real togetherness shown in particular after succesive wins against Southampton, Wolves and Watford, and Jackson feels that will remain important in the remaining four games: "From my experience, what I've seen as a player, as a coach, the crowd can pull a team through just by their reaction.
"You've got to give them something, but sometimes they can realise when you need something as well, and this group of fans have done that brilliantly, and we need that to continue.”
Everton’s supporters have also been praised for the way they have got behind their side, certainly at Goodison Park, and while Burnley may not have the same size fanbase, Jackson added: "It doesn't mean they don't care about the team, they care just as much as any club's supporters.
"They may say we're not as big as Everton or whoever it may be, but they are your fans, it's their club.”