"There's no end to my job. We keep stretching and stretching, but there's always more to do," he says.
Still, scratch the surface, and you find that Mr Walsh is an unsung hero at Amex's European headquarters in Brighton.
The reason is simple. In the past service companies didn't worry much about the kinds of costs with which procurement managers typically deal - everything from paper clips to mainframes. But globalisation is forcing efficiencies across the board - even in profitable service companies.
The solution has been outsourcing, and the difference between managing a good or bad outsourcing programme can materially add or detract from the bottom line.
A recent study by the consultancy group Lorien, conducted in conjunction with the Chartered Institute of Purchasing and Supply, shows just how cutting edge Mr Walsh is.
Lorien asked 720 purchasing managers from across Europe to assess their company's performance across key purchasing and supply areas. Lorien's conclusion: "Service companies overall rated themselves behind manufacturers in terms of procurement expertise."
Up to a point this was logical. Purchasing agents at manufacturing companies are responsible for 80 per cent of total costs. Purchasing agents at service companies are responsible for only 20 per cent of total costs.
Lorien discovered that service companies plan to recruit more purchasing staff than their manufacturing counterparts. The Chartered Institute of Purchasing and Supply reckons that a 1 per cent cut in costs equals a 10 per cent gain in sales.
Mr Walsh's experience shows the difference this can make to a company. He joined Ford Motor Co in 1978, moving on to purchasing positions at Electrolux and Procter & Gamble. In 1994 he joined Amex while it was going through a round of major consolidation. Before Mr Walsh joined, the company paid many of the bills it owed European suppliers locally. "The company was throwing away the potential leverage it had with suppliers," he says.
Amex had an over-centralised purchasing system that created reams of paperwork, as requests for approvals, and then approvals, moved up and down the chain of command.
In 1994, Amex Europe centralised its technology operations. A year later Mr Walsh moved a team of four procurement people "out of their ivory tower" and located them in the middle of the technology department. "The idea was to get them accepted as part of the team," he says.
When this proved a success - as the procurement people helped Amex Europe's technology department improvement its performance - the company extended the experiment to marketing.
By 1996 Mr Walsh was ready to move ahead with phase two of modernising Amex Europe's procurement programme. The focus this time was on reducing paperwork. He increased the distribution of the corporate purchasing card. People took more spending decisions on the ground - and the company found that this saved money.
The year after that Mr Walsh set out to extend these two concepts to virtually all areas of the company.
His department maintained support from the top by decreasing the procurement spend of Amex Europe, without increasing the budget of his own department.
Last year Mr Walsh extended his focus from the UK to Europe. The procurement department "moved from the dotted line to the solid line" in connecting London and continental procurement operations, he says.
Having introduced what amounts to a procurement revolution at Amex Europe in four years, Mr Walsh is spending this year spreading the gospel. "We're holding seminars now in which operating managers and procurement agents get together over a week to figure out together how to achieve savings," he said.
This involves looking at the supply chain, with a view to taking out costs, obtaining faster delivery, demanding higher specifications, and, where necessary, changing the delivery mechanism.
What does he have planned for next year? "The same programme," he says. "But with a focus on developing our use of the internet."