The grocer's shares fell 1.65 per cent to 226.16p yesterday, adding to a prolonged decline that has wiped out a third of the firm's market value since the start of the year.
Mr Lewis, who joined Tesco a month earlier than planned yesterday, asked the firm's 500,000 workers around the world to email him with any suggestions for improving the firm.
"I'll be looking at all parts of the business. Clearly we all want to see an improvement in performance, but I won't take any hasty decisions," he wrote to staff.
He will spend his first few weeks at Tesco's head office and in "as many of our businesses and stores as possible".
His letter also paid tribute to Philip Clarke, who stepped down as chief executive after three years in charge and a four-decade career at Tesco.
Mr Lewis is the first outsider to lead the company, which has more than 200 stores in Scotland and 3,330 across the UK.
He took the top job after 27 years at Unilever, where he was in charge of personal care brands including Dove, Lynx and Vaseline.
Tesco and the other large supermarkets have lost customers in recent years to the German discounters Aldi and Lidl, prompting them to sacrifice their margins to offer shoppers bargains.
The fallout from this price war has led to two profit warnings in as many months at Tesco, the latest of which knocked six per cent off the retailer's shares on Friday.
Harris Associates, which until recently owned three per cent of Tesco shares, has reduced its stake to about one per cent over the past month.
The US investment manager is concerned about Tesco's lack of clear strategy, according to reports.
Tesco is due to unveil its annual results on 1 October. The firm's sales dropped four per cent and its market share dipped to 28.8 per cent in the 12 weeks to August 17, according to figures from research firm Kantar Worldpanel published last week.