Palmer was promoted from the Under-21s on Monday after Maddison pulled out of the squad with ankle ligament damage, while Bellingham withdrew on Tuesday due to a shoulder problem which kept him out of Real Madrid's game at the weekend.
Sterling, once a Southgate favourite, was overlooked again, despite his impressive form for Chelsea this season and the 28-year-old has now been absent from all five England camps since last winter's World Cup.
"In terms of Cole, the key was [we] lost Maddison and Jude so we wanted somebody who could play as a 10," Southgate said.
"Of course, he’s playing wider at the moment for his club, but we hadn’t lost a winger as such, we’d lost two attacking midfield players. So we’ve got a couple of players now who can fulfill that sort of role for these games.
"Raheem was excellent at the weekend against [Manchester] City, as was Cole. But the position was the reason for [calling up] Cole really.”
Palmer's former City team-mate Rico Lewis has also been promoted from Lee Carsley's U21 squad and will be hoping for a senior debut in the Euro 2024 qualifiers against Malta on Friday and in North Macedonia on Monday night.
“With Rico, at the moment we just see a very good footballer," Southgate said. "So I think he’s probably happiest as an eight, talking to him, but he’s obviously played either full-back position. Quite often at Man City, that’s the full-back going into midfield. So he’s a young player we thought it would be good to have some time with us and we’d be able to get a feel of his attributes and we’d be able to work with him closely."
England have already qualified for Euro 2024, leaving Friday's game against the 171st-ranked side the world as something of a dead-rubber - even if Southgate has impressed upon his players the need for maximum points to help ensure they are among the six top seeds in Germany next summer.
Despite the relatively low stakes, Wembley has sold out for Malta's visit and Southgate says the continued interest in England is down to his players.
"It says what football means to this country, there is no doubt about that," Southgate said.
"There are very few countries around the world that can get an attendance like we will have at Wembley tomorrow for a game against an opponent ranked further down the rankings when we have already secured qualification.
"I think that is huge credit to the players and the way they have played. Their performances in the last World Cup and since the World Cup… they have played exceptionally, scored a lot of goals and been exciting so people are looking forward to watching them play. When I travel around, that’s what people say when they are speaking to me."