Talking to analysts after its first-quarter results, chief executive Ken Murphy said it was working hard to address the shortfall, but conceded it might have to pay more to make up the numbers.
“What I’m hearing is we can manage it and we have to play it as we see it,” Reuters reported.
There were no gaps on the shelves, he added, and product availability in stores remains “really strong”.
“Once there is an understanding that there is the availability of work and rates are potentially more attractive, they will fill very quickly.”
The Road Haulage Association says there is a shortage of up to 100,000 drivers in the UK and largely the result of EU workers leaving post-Brexit.
The trade body met with the government this week to flag its concerns over the situation but said there had not been any resolution.
Earlier, the grocer had revealed that revenue rose 1% to £13.3bn in the 13 weeks ended 29 May, an 8% jump compared to the same period two years ago when very few people knew what Coronavirus was.
Trading benefited from increased at-home consumption during March but slowed in April and May as restrictions eased.
Murphy added that Tesco was also extending its one-hour delivery service Whoosh to eleven more stores as part of its trial.
All items are delivered by bike, moped or car, with a £5 delivery fee.
“We’ll keep testing and learning from this as well as the trial we’re doing in more than 260 One Stop stores with Deliveroo (LON:ROO),” Murphy said.
Shares fell 3.1% to 223.9p.