Sam Allardyce has said Wayne Rooney still has a “massive” role with England but admitted events at Manchester United will determine where and whether the country’s record goalscorer plays and refused to confirm the 30-year-old will remain captain of the national team.

Allardyce was presented as the England manager at St George’s Park on Monday, when it was confirmed his first game will be the World Cup qualifier in Slovakia on 4 September. The 61-year-old cancelled plans for a Wembley friendly against Croatia on 1 September, preferring more time training with a squad that flopped dismally at the European Championship. He announced his former assistant at Bolton Wanderers, Sammy Lee, had rejoined the England coaching staff. Talks are continuing over a part- time coaching role for the Bayern Munich assistant-manager Paul Clement, and the sports psychiatrist Dr Steve Peters will be approached to work with England’s senior team again.

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Yet whereas Allardyce began “the greatest challenge I’ve ever had” with several swift announcements, he was equivocal over Rooney’s position as captain and an automatic starter for England. “It’s a decision that I’ll make once I’ve got my feet under the table,” said the new manager regarding the captaincy. “I think I’ll wait until I meet the players. Put it this way, I still think Wayne Rooney has a massive part to play in the England side. I don’t think there is any doubt about that.”

Rooney’s place, Allardyce admitted, will be influenced by his form under José Mourinho at Old Trafford. Roy Hodgson deployed him in central midfield at Euro 2016 but his successor signalled an immediate break with shoehorning players into the side.

“I think José will determine where Rooney plays,” Allardyce said. “Because if José says he is not going to play him in centre midfield and he’s playing up front and scoring goals for Manchester United then it would be pointless me bringing him into England and playing him in centre midfield.

“He can play that role because he has proved it for Manchester United but you’ve got to ask: ‘What position do they really want to play in?’ Sometimes you have to ask a player not to play in a position they may prefer and they take it on board because it’s for the benefit of us all.”

Despite warning that England’s pool of talent in the Premier League is “smaller than it has ever been before”, Allardyce believes he has inherited a group of players good enough to have won the European Championship this summer.

Facebook Twitter Pinterest Sam Allardyce during the press conference at St George’s Park. Photograph: Alex Morton/The FA via Getty Images

He said: “I think they could have won it had they all performed to their best. I was extremely excited by the performances that came before they got to the tournament. I thought there was some outstanding ability to beat teams with plenty of goals in the side. Maybe we looked suspect defensively at times but we seemed to be able to score one more goal than the opposition. Unfortunately that all seemed to dry up in the tournament.

“I watched the Iceland game in Spain. I was extremely frustrated and disappointed. We shouldn’t have underestimated Iceland. I’m not sure England underestimated Iceland but when you see Albania winning games at the Euros you’ve got to understand the lesser countries are so good at organisation now. Wales is a perfect example by getting to the semi-finals. The so-called smaller nations are not as easy as people make out.”

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Allardyce signed a two-year contract with the Football Association on Friday – “There is the possibility of another two years after that,” he said – but the reality of fulfilling a career ambition hit home only on Monday when driving to Burton and St George’s Park.

The former Notts County, Bolton, Newcastle United, Blackburn Rovers, West Ham United and Sunderland manager showed rare emotion and his voice briefly faltered as he said: “It’s been a whirlwind few days. Waking up this morning, and on the drive down, the reality of what is resting on my shoulders dawned and I will be the man most focused when the internationals come around.

“It’s the greatest challenge I’ve ever had and I look forward to it so much even with all the pitfalls there might be. It’s my time, my chance and I’ve waited a long time for it, a long time. It’s arrived. I suppose at 15 I never thought I’d be sat here. I celebrated quietly at home with a few friends and family. It was a very interesting weekend.”

The FA has spent several years promoting possession-based football at all age levels with England but the new man in charge of the senior side said: “My job is to get the players in each position and as a team to win a game of football in whatever way needs to be done in any particular game.”

Allardyce admitted he had a responsibility to all English coaches. “The England manager should always be an Englishman, for me, and it’s for me to try to help promote English coaches throughout the country in the hope we’ve got a succession of English managers who could end up running the national team. My first priority is the first team, there’s no doubt about that, but beyond that I hope I can help.”