Sam Allardyce believes England’s players are emerging from the ordeal of their calamitous defeat by Iceland at Euro 2016, despite the manager admitting he has seen for the first time how the pressure of playing for the national team can hold them back.

Allardyce said he had inherited “a happy bunch not a damaged bunch” but, having won his first match with Adam Lallana’s stoppage-time goal in Slovakia, he also talked about the deterioration in the players’ mood on the morning of the match – a legacy, he said, of what had happened in France in the summer.

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“I think they were probably a bit nervous,” Allardyce said. “I saw a little nervous tension. It [Iceland] is bound to be in the back of their mind, isn’t it? They had a holiday, a pre-season, started the season with their clubs and then it comes to the first England game after Iceland and maybe there was nervous tension.

“It was too negative in the first 45 minutes. I think it was possession for possession’s sake rather than trying to break the opposition down. That was maybe sub-conscious, players thinking: ‘I don’t want to be the one who gives that ball away.’ I could see that: ‘What if I make that pass? Oh, I don’t know …’ But we have to be brave.

“I haven’t asked what their biggest fear is because I didn’t want to talk about fear. I wanted to be positive and tell them what the future is. The only thing I mentioned about the past was to learn from it and the only thing I said was don’t feel like that again next time around.”

The Football Association is no longer using Steve Peters, the Liverpool club psychiatrist brought in by Roy Hodgson for England’s past two tournaments, and has turned to the sports management company set up by the Olympic gold-medallist swimmer Adrian Moorhouse.

One of its sports psychologists, Jonathan Zneimer, has already been involved with England teams at every age group from under-21 down and Allardyce recognises the importance of working on the players’ minds after Euro 2016 ended with Greg Dyke, the FA’s then chairman, saying the players “froze” and “were scared”.

“It is different in terms of Steve Peters,” Allardyce said. “This is a company with many facets in their locker. We will use them on a consistent basis to help the players build resilience so they are able to cope with pressure better. Even though they already deal with a lot of pressure, on an international stage it’s a different type of pressure and they are very young. As a squad we are really young and as human beings, when we get criticised, we hurt – we really do.”

The pain of Euro 2016 has by no means subsided, according to Eric Dier, whose assessment of its impact on the squad somewhat contradicted Allardyce’s and was a good deal more downbeat. “There is a long way to go until the scars have been healed but it is a start,” the midfielder said, reflecting on the victory in Slovakia. “All we can do is win against whoever we have in front of us but I think there is a long way to go before we repay everyone for what happened in the Euros. And for ourselves as well because we were the most unhappy of everyone and there is a long way to go until we are happy again.”

Lallana’s first international goal spared England another wave of criticism but Allardyce’s team had struggled until Martin Skrtel’s sending-off and benefited ultimately from a goalkeeping mistake. England did not manage a shot on target until the 64th minute and Harry Kane admitted the team’s lack of confidence in the final third may be a hangover from the tournament in France.

“It could be,” the striker said. “It is difficult sometimes when teams like Slovakia drop off and make it very difficult to play through – you have to be very patient and make sure that ball is spot on every time.”

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Allardyce opened himself to scrutiny after the game by declaring he had given Wayne Rooney carte blanche to play where he wanted. The manager went on to say he was surprised Rooney operated in such a deep role – “He’s not to forget we want him to score goals” – but it was clear the manager was willing to give his captain special privileges.

“I am using his experience to its maximum on the field. He has had it at Manchester United, under many different managers, playing down the right, the left, centre-forward, in behind, centre midfield. Mine and Wayne’s relationship, as we grow, will always be to promote him wherever he plays.”