Gareth Southgate said he has proved he can “handle big occasions” after his four‑match stewardship of the senior England side ended with an encouraging if ultimately frustrating draw against Spain.

His team conceded two late goals, Isco’s equaliser coming five minutes into stoppage time, to temper some of the optimism whipped up by the most impressive display of Southgate’s short tenure. The process to appoint a permanent successor to Sam Allardyce will begin in earnest on Wednesday, with a five-man selection panel – comprising the FA’s chairman, Greg Clarke, the chief executive, Martin Glenn, plus Howard Wilkinson, Dan Ashworth and Graeme Le Saux – expected to recommend the 46-year-old takes over on a four-year contract with a break clause applicable after the 2018 World Cup.

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Southgate, acutely aware he will return to the under-21s if he is not taken on, would not be drawn on whether he wants the job but has made it clear privately he would like to continue what he has started. “I’ve not learned anything about myself but I’ve learned a lot about the role and relished the challenge,” he said. “I’ve proved I can manage big matches, that I can tactically – with the help of my staff – prepare a team to play against a top side and give them a tough test. I’ve proved I can handle big occasions.

“I feel every situation I’ve been through, and many have been complex and potential powder kegs, we’ve coped with very well. And I’m pleased with how we’ve coped with it all really. More than that, we’ve built some important stability for the group of players and the team. It’s been a brilliant experience for me. I’ve thoroughly enjoyed working with the players and can see the potential of the group. I took over at a moment of instability for everybody, and we’ve brought stability back and built a platform for the team.

“In terms of the remit, we’ve fulfilled that. It’s an exciting group of players. They’ve got a lot of potential but there’s a long way to go before we can be considered a top team. I’m proud to have led the country for a couple of really important games and experienced what that feels like. We’ve got a European Under-21 Championship next summer and the draw is being made next month, so I need to know where I’m going to park my car for the next few weeks.”

Southgate saw positives in his team’s display, with England the better side for long periods. “I definitely took encouragement,” he said. “The players, over the period of the four matches, couldn’t have given any more. I’m really pleased with them, especially the way we were tonight. We had long discussions before the game about our approach, wanting to be a front-foot team pressing high. If we were going to be defeated it was going to be being positive and brave without the ball. At times we did that well.

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“That comes with a price as the game goes on. At times we kept the ball well and were certainly a threat in transition and counterattack but maybe in the second half we weren’t able to keep it quite enough. You pay the price. We were fatiguing in the last 20 minutes, and they are a top side. It feels like a defeat for the players but I couldn’t be prouder of their efforts. It was a healthy, positive performance. Maybe not winning will be better for us in the long run, knowing what we have to do at this level.

“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. They have the potential to go and do that longer term. They now know the benchmark. We made changes [on the pitch]ourselves as well, and maybe lost a bit of cohesion towards the end. But what a brilliant experience for all of them. It should start to build belief in them as a group.”