Everton may have just broken their transfer record to sign £45m Gylfi Sigurdsson from Swansea City but as far as Ronald Koeman is concerned the club still has business to do before the transfer window closes.

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“We still need to sign a striker,” the Everton manager said. “Everybody knows that we lost Romelu Lukaku. We brought in Wayne Rooney, Sandro Ramírez and now Gylfi, and maybe they can share the goals around more than happened last season, but we still need another one to play the No9. When you play in Europe, and let’s hope we reach Europe, and in the Premier League you cannot do it with just one or two strikers.”

Everton, whose summer spending now stands at £131m, were linked with Arsenal’s Olivier Giroud last month, though the French striker appears to have made his peace with Arsène Wenger, and Koeman no longer believes there is any possibility of a deal. He admits time is running out and that it is difficult to sign top quality players when you cannot offer Champions League football – unless they can deal with the threat of Hajduk Split in the play-off round that begins on Thursday Everton will not even be in a position to offer Europa League football – but remains hopeful at least one of his targets will be landed before the end of the month. Koeman would also like left-sided cover for Leighton Baines in defence, though a striker is a clear priority.

“We have signed Sandro and Wayne, and we know the development of Dominic [Calvert-Lewin], but we are looking for an extra striker and it is difficult because it needs to be a player of a certain quality or a young player who can improve,” Koeman said. “We know we have the possibility to sign good players but we don’t play Champions League and that sometimes makes decisions very difficult.”

It was never a difficult decision for the Everton manager to go after Sigurdsson, a player he tried to sign when in charge of Southampton, though Koeman did admit to finding it surprisingly hard to let go of Gareth Barry, who has joined West Bromwich Albion in search of more regular football and the five games he needs to pass Ryan Giggs’s all-time record of Premier League appearances.

“We tried when I was at Southampton to sign Sigurdsson but we did not have the finance that we have here at Everton,” he said. “In my opinion, in his position, he is one of the best players in the Premier League. We want more productivity in the team after losing Lukaku and that is exactly what Gylfi brings. We have worked a long time to get this deal done but he is one of the key players we wanted to bring in. Last season apart from Lukaku we did not have one player who scored 10 goals. Now, with Gylfi, Wayne and Sandro, we think that might be different.”

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Koeman revealed he had been open to keeping the experienced Barry in the squad but the player realised he faced much stiffer competition for first-team places.

“You never want to lose a top professional like Gareth but I could understand his position,” he said. “He knew he would not be appearing every week and he is still the type of player who wants to keep playing. I let him go because I respect him, but I still had to ask myself whether we had enough midfield cover. I think we probably have, with Morgan Schneiderlin, Tom Davies and Muhamed Besic, maybe even Davy Klaassen if necessary, but of course I don’t know how the season will go so I don’t have that answer now. Maybe I will get a headache one day wondering why I let Gareth go.”

Koeman is open to loan moves as well as a permanent transfer – although he laughed at the suggestion Diego Costa might be a possibility – and is pleased with the business done in the window so far. “We have brought in some good young players in important positions and that is good for the future of the club,” he said. “We are still trying to get more but they have to be of the best quality. We don’t sign players just to get numbers in.”