England had to come from behind to beat Slovakia 2-1 and to close in on next year’s World Cup finals.
Slovakia stunned hosts England in the third minute when Stanislav Lobotka punished some slack defending to prod the opener past keeper Joe Hart.
Eric Dier calmed the home jitters with a well-taken 37th minute equaliser before Marcus Rashford’s stunning 59th-minute winner.
But a frustrated Alli ended the game on a sour note after he gave referee Clement Turpin a middle-finger gesture after not getting a foul.
However, Southgate is yet to see the incident, which could see Alli retrospectively punished.
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He said on the Alli gesture: “You’ve only just told me just before we started. I’ve not seen it but obviously we’ll look at it over the next couple of days.”
The England head coach was pleased with the way his players reacted to going down so early on.
Southgate added: “We didn’t start the game well but I was pleased with the way the players reacted on the field.
“They got themselves into better positions. We were stretched in the first 15 minutes or so.
“Great credit to the players for staying in the game and then in the second half we were in control. We didn’t give them space to play.
“Rashford showed everything he has tonight.
“At times he has to do better but his work on the ball, the maturity of his performance and his ability to go past people was devastating to the opposition and lifted the whole crowd.
“I’ve not seen the Dele Alli incident. We have to finish the job tonight.”