The Football Association is increasingly open to the idea of Gareth Southgate taking the England job on a full-time basis despite the two disappointing performances so far in his brief period as caretaker manager.

Southgate has impressed his employer with the manner in which he has approached the job since he was promoted from his usual position with the under-21s in the aftermath of Sam Allardyce’s departure and there is a feeling within the FA that it would have been unfair to expect too much improvement in the games against Malta and Slovenia.

While Southgate has been candid enough to recognise both performances could have been considerably better, he has also talked about inheriting “a mess” on the back of Allardyce’s ignominious 67-day spell in charge and England’s galling experiences at Euro 2016.

He has subsequently backtracked on that word, saying he should merely have called it “difficult circumstances” but the FA does recognise there are mitigating factors. Southgate’s chances of being offered the job properly will hinge more on England’s games against Scotland and Spain next month and the former Middlesbrough manager sounded like he was growing into the idea of taking on the position, in stark contrast to his admission after Roy Hodgson’s departure about not being ready for it.

“It’s been a remarkable experience,” Southgate said. “I feel stronger and more confident for it, and I recognise the responsibility it brings.

“I could not have been happier with the approach of the players or the staff, and I think we have prepared them to be in the best possible place to get the results we wanted. That hasn’t quite happened, but I would temper that by pointing out everything they have had to contend with.

“I haven’t had charge of the team before. I had not been preparing for these two matches until the last two weeks and I had not worked with all of the staff or the players before. With all the injuries as well, there have been so many things we have had to deal with over 10 days.

“It was difficult for anybody to know what success would have looked like 10 days ago because there was so much to take on board. I have to be realistic about how much progress you can make in that situation, on the back of what was a difficult summer for everybody. But I see huge potential in them as a group, a real willingness to work, a real desire to play for their country and a real pride in playing for their country.

“They are not going to get everything right at the moment and their heads were down [after the Slovenia game] because they know the expectation to win. I don’t want to take that away. We want to aim for excellence. There are things to improve on, but I do have to temper that with what must have been a difficult situation for them as well.”

The FA likes the calm way Southgate has approached a difficult situation and the caretaker manager also appears to have the backing of his players, with the stand-in captain Jordan Henderson among those voicing support after the goalless draw in Ljubljana.

“The players have got on really well with him,” Henderson said. “The manager has been brilliant with us, so we need to put in the performances not just for ourselves but for the fans and him, and the coaching staff as well, to make sure we keep working together for a long time.”

Southgate intends to watch the midfielders Ross Barkley and Jack Wilshere in the next few weeks to determine whether they deserve to be recalled but he does not anticipate many changes for his next squad – “I’m not sure how many other players there are” – at a time when he does “not think any of the under-21s are ready to move up just yet”.

England play Scotland in a World Cup qualifier on 11 November followed by a friendly against Spain, also at Wembley, four days later. “I feel pleased with how I have handled a number of situations,” Southgate said, when asked directly if he wanted the job. “That’s been a great challenge because it’s obviously a level up from what I have had to deal with before. I feel confident. The rest needs serious consideration from everybody’s point of view.”