During his tenure, England won two games and drew two, scoring seven goals and conceding two.
"I've proved I can manage big matches... I can tactically, with the help of my staff, prepare a team to play against a top side and give them a tough test," he told reporters after the 2-2 draw at Wembley.
The 46-year-old, who was handed temporary charge after Sam Allardyce was sacked on Sept. 27, said he had introduced stability to the team after England's disappointing European Championship campaign.
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"I took over at a moment of instability for everybody, and we've brought stability back and built a platform for the team," he added.
"Without doubt, the longer you work with any team, with any group, you have the chance to embed more ideas, review each game and learn from it. The players are bullish about how they want to play."
Southgate, who was in charge of England's under-21s before being elevated to senior manager, urged the English Football Association to decide his future quickly.
"We've got a European Under-21 Championship next summer... so I need to know where I’m going to park my car for the next few weeks," he said.
An Adam Lallana penalty put England ahead in the 9th minute, before Jamie Vardy doubled the lead soon after the interval, but Spain scored twice in the dying minutes to draw level.
England's next game is a friendly against Germany in March.
(Reporting by Debanjan Bose in Bengaluru; Editing by Andrew Both)
