The Parkhead manager hasn't spared his players in the days since the 3-2 defeat at Hampden but he has been angered by some of the wider media reaction.
Lennon declined to specify who his comments were directed towards, as he looked ahead to tonight's Clydesdale Bank Premier League meeting with Kilmarnock, but they appeared to include a reference to the former Celtic player Murdo MacLeod, who wrote in a newspaper column that "blowing two trebles" was "verging on criminal".
Lennon also took umbrage at the Kilmarnock manager Kenny Shiels' suggestion that Celtic had "underachieved" in comparison to his own team,
"I think I have a right to be critical," Lennon said. "I think I am the only one really who has a right to be critical of the team when they perform like that. Supporters can have their say, but I am not overly enamoured with columnists and yada yada yada having a go at the team.
"When we lose a game, they seem to come out with the usual sycophantic lines like, 'we feel sorry for the fans who have spent their hard-earned cash, blah blah blah'. They don't really care about the fans who have spent their hard-earned cash at all.
"I am not going to name names, but his opening line was 'to lose one treble is careless, to lose two is whatever'. It was as if winning a treble is as easy as shelling peas. He is trying to drive a wedge between the players and the fans with that comment about the hard-earned cash – I think this team has given value for money this season to the supporters, as they have done for the last couple of years.
"They have played the best football and we have been in semi-finals and finals and challenging for the league on a regular basis. And we have spent very little, so for people like that to come out and have a pop – and you never see him here unless Henrik is about the place – it irks me. I am sure he didn't spend any money going to the ground and getting to the game.
"I don't like that when they try to drive a wedge and get on their high horse and moralise to everyone when they know how difficult it is. There are only two managers who have won a treble in the history of his club [Jock Stein and Martin O'Neill], so I think that speaks volumes for how difficult it is."
Tonight's match at Parkhead comes just over 24 hours before the closure of the transfer window, with Celtic wary of a further Norwich City bid for Gary Hooper. Two have been rejected and Lennon was adamant any third offer would be treated the same way.
He regards rumours of an imminent bid from Tottenham Hotspur as mere speculation. "People are working hard down the road, maybe to unsettle the player for their own reasons," Lennon said. "Everyone has a price but the timing would be so wrong for everything we want to push forward with.
"We have had two bids in from Norwich and that's been it. It won't surprise me if another comes in but the answer will be the same. Peter [Lawwell, Celtic's chief executive] is with me on it. We spoke about it yesterday. He expects bids to come in but the answer will be no."