The 21-year-old has become one of the key players in Enlgand's squad and he is expected to get more responsibility after Rooney´s retirement.
"Dele is an exciting player and it's a great opportunity for him to kick on, but there's always a challenge", Southgate said.
"Like all young players, he's got to keep looking to improve. His goalscoring record over the past couple of years is phenomenal for a player who is not an out-and-out striker", the England manager added.
Alli has not yet won any trophies with Spurs, but the midfielder played a major role under Pochettini, as his side finished in second place in the Premier League last season.