Lord Robertson of Port Ellen, who served in the post from 1999 to 2003, told peers there is a need to ensure the West is not nervous of Russian escalation.
Instead, the UK and its allies “need to breed” in military chiefs in Moscow the worry of a possible conflict with Nato – something he said Russia “could only lose”.
His remarks came as peers debated the situation in Ukraine and pressed for Western countries to develop a long-term strategy to aid Kyiv.
Ukraine is pushing for Nato membership, although this remains a thorny issue for some of its current membership.
Nato’s collective defence guarantee, known as Article 5, means an attack against one ally is considered as an attack on them all.
Lord Robertson highlighted the “enormous propaganda exercise” being undertaken by the Kremlin in a bid to “undermine Western support and encourage the global south countries to bend to them”.
He warned it is “already having an effect” on European opinion, as he pointed to a poll which suggested a majority of Hungarians, Romanians and Bulgarians believe providing weapons to Ukraine “provokes Russia and drags their own countries closer” to the war.
Lord Robertson, referring to Russian president Vladimir Putin, said: “It was one man who took the decision to invade and it will take one man to decide enough is enough.”
The former defence secretary cited examples of the former Soviet Union in Afghanistan and authoritarian leaders taking steps back when they could see the “ground was moving under them”, adding: “Personal survival matters to them much more than saving face.
“That’s why it’s imperative that Vladimir Putin gets the same message, and that he will get it by the West standing firm and resolute and with Western leaders regularly and loudly telling their people what’s at stake and why sacrifices are in their own personal and nation’s interest.”
Lord Robertson highlighted the Russian effort to produce military supplies and said it is “crucial” the UK and its allies supply Ukraine with the weaponry it requests.
He went on: “And I say again that we need to guard against that fear, that apprehension of escalation in so many leaderships in Europe.
“Instead of the West being nervous of Russian escalation, something that they’ve maxed out already, we need to breed in the military hierarchy in Moscow the worry that if they overdo what is being done in Ukraine then an actual and not fictitious war with Nato might be the result; a war that they know they could only lose.”
Lord Robertson said his experience of the Russian military is they are “very patriotic and very conservative”, adding: “The motherland is more important and in the end they will not be prepared to risk the motherland for a failing Putin-esque adventure, and especially one which has been so spectacularly unsuccessful and wasteful and indeed humiliating.”
Lord Stirrup, who served as head of the Armed Forces between 2006 and 2010, earlier said relations between the West and post-conflict Russia and Mr Putin cannot resume “as if nothing has happened”.
The independent crossbench peer said: “It must accept at last that it is dealing not with a normal government but, as I publicly asserted nine years ago, with a gangster regime; a regime that will tell any lie, betray any promise and commit any crime in pursuit of what it sees as its interest.
“The West must respond accordingly, it must impose an appropriate cost on Russia and that will inevitably have long-term consequences for international relations.”
Independent crossbencher Lord Skidelsky said the war aims from the UK Government are “unachievable”, saying: “Ukraine isn’t in a position to fight the kind of war it can win.
“Its over-hyped counter-offensive has stalled and most military experts believe inconclusive trench warfare will be the order of the day for months to come, and in those circumstances there will be a strong temptation on our side to break the stalemate by progressive scaling up of warfare.”
Defence minister Baroness Goldie, concluding the debate, said the UK and its allies must show their support for Ukraine is “iron-cast” and “unflagging”.
She said: “The Government has been very clear that we must continue doing all we can to support Ukraine … Mr Putin must be defeated – that is the only route to Ukrainian and global security.”
Lady Goldie added: “In the end, conflicts can only be resolved through a negotiated settlement, a settlement whose parameters will be set by Ukraine itself, a settlement that begins with Russia withdrawing from all Ukrainian territory.”