England had already qualified for the European Championship with two games to spare, but they are bidding to secure a place among the top seeds in Germany by winning Group C in style.
Only the top five best performing nations throughout the qualifying campaign will be top seeded in next month's Euro draw.
Unbeaten England have six wins and a draw in the group after Enrico Pepe's early own goal and Kane's second half strike settled a drab encounter at Wembley.
A victory in their final qualifier in North Macedonia on Monday would achieve England's top-seeding target, with a point possibly enough depending on other results.
Given Malta's lowly 171st place in FIFA's world rankings, this was by far England's least impressive performance in a qualifying campaign that has otherwise been plain sailing.
Conor Gallagher was taken off at half-time after a tepid display, while Marcus Rashford's Manchester United struggles continued for England.
Trent Alexander-Arnold was one of the few bright spots playing in a midfield role instead of the right-back berth he occupies for Liverpool.
"If you don't start games well, it's very difficult to pick it up and we didn't. We know the level we've got should be better," Southgate said.
"Not enough quality on the ball and not enough chances created. We didn't hit the heights that we have this year.
"We have a lot of players that weren't in there tonight. The number of games these players are playing, it's almost a self-regulation.
"There are positives, but we know we were not where we want to be."
It was hardly the ideal way to pay tribute to former Manchester United and England star Bobby Charlton, who died aged 86 in October.
Southgate was at Charlton's funeral in Manchester on Monday and the 1966 World Cup winner was celebrated prior to kick-off against Malta.
In England's first home game since Charlton's death, a video montage was introduced by his World Cup team-mate Geoff Hurst, while a red and white mosaic in the stands read 'Sir Bobby'.
Lethargic England
Fans in the sell-out 80,000 crowd lit the torches on their mobile phones as the video played before the teams gathered in the centre-circle for a period of applause.
In a sign of the England lethargy to come, Malta could have been ahead in the first minute when Gallagher gave the ball away to Teddy Teuma, who drove forward before firing just wide from the edge of the area.
Sparked into action by that narrow escape, England went in front after eight minutes.
Phil Foden raced into the area and his cross towards Kane was accidently diverted into his own net by Pepe, the ball hitting the defender on the shin before looping in off Malta keeper Henry Bonello.
However, that fortuitous breakthrough was not the trigger for the expected England goal spree, as Malta kept the hosts at bay for long periods.
It was the first time England had failed to record a shot on target in the first half of a home international since a friendly against Germany in 2017.
Chelsea forward Cole Palmer came on for his England debut after an hour, with Jordan Henderson again jeered by a small section of fans following his controversial move from Liverpool to Saudi Arabia.
With bored supporters throwing paper aeroplanes onto the pitch to entertain themselves, Alexander-Arnold finally had England's first shot on target in the 65th minute but Bonello was equal to the effort.
England at last doubled their lead in the 75th minute when Kyle Walker and Foden exchanged passes to open up the Malta defence.
Foden found Bukayo Saka and his low cross was coolly converted by Kane from close-range.
