Sainsbury’s on Thursday said it was facing a £140m hit from the NI changes.
Lord Rose’s warning came as he said Asda was racing to make its supermarkets competitive again.
He said Asda had taken “a slight step back” in recent years in terms of its performance. Since Asda’s takeover by the billionaire Issa brothers and the private equity firm TDR Capital in 2021, its share of the grocery market has slipped from 14.8pc to 12.6pc.
In September, Lord Rose said he would take over the day-to-day running of the business, with Mohsin Issa formally stepping back as chief executive.
In an update on Friday, Asda said like-for-like sales were down 4.8pc in the three months to the end of September compared with a year earlier, which it said was an improvement on the previous quarter.
Lord Rose said: “We’ve been going through this massive change program on transformation. It has distracted us a little bit probably from what we should or what we would normally do.”
“Shopkeeping is about doing the right things for our customers. You’ve got a couple of shopkeepers now, in terms of Rob [Hattrell, TDR partner and Asda director] and myself looking at stuff.
“What we think is that we need to improve our store experience, we need to improve our availability, and we need to sharpen our prices.”
Asda said it would spend another £13m on increasing staff hours before the end of the year to improve customer service.
Earlier this week, Asda said it was cutting 475 jobs to remove duplication and simplify structures in its teams.
It is also ordering staff back into the office at least three days a week, in a step bosses claimed brought it more in line with rival supermarkets including Tesco and Morrisons.
Lord Rose on Friday said: “We sadly had to make some changes this week in terms of structure … I absolutely fundamentally believe it’s the right thing to do for the business.”