Solskjaer then backed Martial to be a big influence for Manchester United, saying: "It's a confirmation that we are happy with him, we believe in him he's got fantastic potential, he's had ups and downs he's been top scorer, he's been developing, as a young lad moving overseas it's not easy but he knows he's going to stay here for the coming future and I believe in him".
"The Europa League is also a very important competition and we want to win it because we think we deserve to a trophy this season".
"Obviously we drew the game but it's just not good enough".
The Gunners will carry a 3-1 lead into Thursday's second leg of their semi-final away to Valencia.
He played a big role for the Magpies who were able to retain their Premier League status with four league games to go.
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"We knew it is going to be hard but our focus is now the Europa League", he told the BBC.
He ranted: "Watch this Huddersfield team, they haven't got the quality".
However, he made amends on the hour mark when he launched a long ball upfield - following a poor United corner - which Luke Shaw failed to intercept and Isaac Mbenza coolly slotted past David De Gea.
In the match against Chelsea, Solskjaer opted for Alexis Sanchez ahead of Martial, who was on the bench, amid suggestions that the club manager was not impressed with his attitude during pre-game warm-up.
"We knew it is going to be hard but our focus is now the Europa League", Arsenal manager Unai Emery, whose side lead 3-1 going into the second leg of their semi-final at Valencia next week, said with an air of resignation.
Barring an astonishing Spurs collapse, the only issue that remains to be decided in the Premier League is the destination of the title.
At the last count, Martial as not included in United's last two games against Huddersfield last Sunday and in the previous match Chelsea before that that ended 1-1.