Ole Gunnar Solskjær has admitted Manchester United are “one down” on the desired number of strikers after failing to sign a replacement for Romelu Lukaku.

The centre-forward was sold for £70m to Internazionale, who have also taken Alexis Sánchez on loan, and, though Solskjær wanted to sign a goalscorer, he did not find the ideal player.

“We are one down, to be fair, but we just didn’t find the right one,” the manager said. “We didn’t find the answer that we wanted.”

He admitted a lack of ruthlessness was a factor in last Saturday’s defeat by Crystal Palace. “We are creating but of course you are always looking for someone to improve us and we were looking,” said Solskjær. “It’s about taking the chances. We have created enough in the first three games to have nine points so we have to be more clinical, we have to work on the last pass, the last finish, but we have created enough chances to win – and maybe score penalties.”

Solskjær may target a finisher who scores “scrappy goals” or a traditional centre-forward, in Lukaku’s mould, should he wish to change the system.

“I do like the one who scores scrappy goals in and around the box – a young Ole or something,” Solskjær said, referring to himself. “It doesn’t have to be a 1.95 [metre] centre-forward. It could be sometimes if we want to play with two up, maybe a different type to what we have.”

In addition to Marcus Rashford and Anthony Martial, who is injured for Saturday’s trip to Southampton, Solskjær says he trusts the 17-year-old Mason Greenwood to help fill the void left by Lukaku.

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“He is a natural footballer. He is enjoying his time on the pitch, he comes alive when he gets closer to the goal, which is great to see in finishing sessions. And he is always the one who ends up in the last two [when the strikers compete in training] – he always scores the goals.

“He is not scoring scrappy goals, I’ve got to say. He’s got proper goalscorer’s goals and he also has to learn that scrappy bit inside the six-yard box – stick your head in where it hurts.”

Solskjær said the departure of Sánchez was necessary. “Alexis needed to go – at the moment we know he’s been here for 18 months and it’s not really worked out for him. For him to restart and get himself playing regularly and scoring goals, that will only benefit everyone.”

The manager defended Jesse Lingard, whom he replaced against Palace early in the second half and who has not scored in the league since 22 December.

“Jesse has never been the most prolific,” he said. “If you look throughout his career he has other attributes and Jesse’s contribution this season has been fantastic. From his first day in training he has shown that he is determined to stay in the team, to show me that he wants to because his application in training and in games [is impressive].

“Of course sometimes you want him to be more in front of goal but he does so much other stuff. I left him out against AC Milan [in a pre-season friendly], he scored when he came on, and he scored 2 the day after when we played Blackburn here [closed doors game]. He can take criticism, being left out because he has the right character to bounce back. I pick him, Gareth [Southgate, England manager] picks him, he knows he is a good player and we value him.”

Matteo Darmian is set to join Parma for €1.5m (£1.4m) but Solskjær said Marcos Rojo was “staying definitely”. Chris Smalling was pictured in Italy holding a Roma scarf prior to completing his loan move to the Italian club.