The peer, who faced fierce criticism as leader, told the BBC a focus on whether Mr Miliband was a "geek" or was guilty of "fratricide" was "irrelevant".
But Lord Kinnock said Mr Miliband was not "destabilised" by the remarks.
Earlier this month, Mr Miliband was criticised by his former adviser, Labour peer Lord Glasman, who complained that the party had "no strategy, no narrative and little energy", while the leader himself had "flickered rather than shone".
'Noises off' And he has faced critical newspaper headlines in recent weeks, a poll bounce for the Conservatives following David Cameron's EU veto and one YouGov poll suggesting the Labour leader's approval ratings were at their lowest yet.
Mr Miliband himself has brushed off criticism, describing it as "noises off" and insisting he has "a strong inner belief" that Labour would win the next general election.
Lord Kinnock Former Labour leaderHe is characteristically so cool and so calm that I'm massively impressed by it”
"Ed is highly intelligent. His intellectual strength is one of his greatest accomplishments. He is courageous," Lord Kinnock said.
"But a section of the press has decided that for some reason he doesn't fit the mould into which they want to pour him and consequently he's the subject of attack."
'Guts' He added: "If they are going to attack Ed, let it be on issues of substance, let it be on policy rather than on stupid things like: is he ugly, or is he a geek, or did he commit fratricide [Mr Miliband beat his brother David to the party leadership] - all of which are entirely irrelevant but constitute the main coverage of Ed Miliband."
Lord Kinnock - who was Labour leader from 1983 to 1992 - said there were "gossips" and "self-serving fools" in all parties.
- The Week in Westminster on BBC Radio 4
- Saturday 14 January at 1100 GMT
Lord Kinnock said he had been hurt by personal attacks during his time as leader and been "merciless" in response, but Mr Miliband was "different" and "happily, less aggressive".
"I've no doubt he notices the attacks. But he is characteristically so cool and so calm that I'm massively impressed by it," he said.
"It is a characteristic of his that I knew a long time ago and is put into practice now in very heated and pressurised conditions.
"And he still - without in any sense being arrogant or complacent, quite the contrary - deals with it, manages it and keeps his focus firmly on the basic issues of concern rather than being disturbed or destabilised by these attacks.
"I think that's an admirable quality and certainly one you need in a leader."