However, the former Crystal Palace owner insists Rodgers' words do not mirror those of Scott Parker's, whose outburst about a lack of transfer activity cost him his job as Bournemouth manager earlier this week.
The Foxes' 1-0 defeat to Erik ten Hag's side has left them rock-bottom of the Premier League with just one point from five games.
In his match programme notes, Leicester chairman Aiyawatt Srivaddhanaprabha told fans that the club's position is secure but net spend over the past few seasons meant they had to tighten their purse strings this summer.
In a post-match interview, Rodgers told BT Sport: "To have to watch every club in the top five leagues get players in and for us not to be able to improve, that was difficult.
"It's not just as a manager but for the players, because they want to compete. This group has shown they can compete but we needed help. Unfortunately we haven't been able to get that."
When quizzed on the current plight Rodgers finds himself in, Jordan reserved a degree sympathy but suggested Rodgers should have steered his side to a higher position in the table.
Jordan told talkSPORT: "The tragedy of that instance is that Brendan Rodgers is in a very difficult position where he can't improve the squad. But that squad of players is still good enough to be more competitive than they're currently being.
"They were slightly unlucky against Brentford and they've been in the Chelsea game. They should have gotten more points than they've got. There's enough in that team to be better than they currently are."
Jordan was then asked what he would have said to Rodgers in the aftermath of the interview, if he had been Leicester chairman.
He said: "I'd tell him to shut up, I'd say, 'If you don't like it Brendan, then you don't like it' but I suspect Brendan has some legitimacy in what he's saying but I don't think it helps anybody by saying it."
Jordan was critical of Scott Parker following his dismissal this week for speaking out against Bournemouth's owners but believes Parker's situation and that of Rodgers' are entirely different.
"I'm a huge admirer of Brendan Rodgers. I believe he's been sold something different. I do not believe Scott Parker was sold anything different," said Jordan.
"I think Parker was given a memo clearly explaining what Bournemouth's expectations were and Brendan was brought into Leicester City, I suspect, with a very different dynamic which is Leicester City are a competitive team in the Premier League who are doing very well and recently won it.
"Who did Bournemouth sell to recoup any money? Leicester have sold Fofana so there's a reasonable trade off [from Rodgers] saying, 'Can I have some of that back'. If you spend nothing you're going to be in a situation where you feel disadvantaged."