Martial, who has scored four goals in seven Premier League games this season, was named as the man of the match after the game - and he admitted that he is happy with how he has been performing of late.
The United boss was happy to collect a much-needed three points against Everton but refused to paper over the cracks.
"Nobody should be surprised by how he is playing with his talent", Pogba said of Martial. Yes, we are good friends.
If this is the team to play Everton, then United will make two changes from the defeat to Juventus last Tuesday in the Champions League. Some teams without the ball, can resist and keep a clean sheet all the time.
Questioned on his weird run-up, Pogba replied: "I always try and destabilise the keeper, maybe they know how I take penalties". In football it's hard to feed that relation with managers, because our life is not an easy one and it's not like we can have conversations or be together every day or every week, but he's a good boy.
Three minutes into the second half, Pogba was involved again for United's second, brilliantly finished by Martial with a curling right-footed shot from outside the box, reminiscent of his second goal in the 2-2 draw at Chelsea last weekend.
"I like the player who says, "I want to take it" like the Crystal Palace player Luka Milivojevic".
'Even without the goal his performance would be a good performance.
'He is understanding things he did not before. You can not score every time you play, there are matches where you are not going to score. Can he improve? I think he can.
Jordan Pickford showed both mental and physical strength as he waited patiently for Paul Pogba to take the spot kick, which the Everton keeper saved with his left hand, but the Frenchman was able to slot home the rebound.
The duo were at the heart of the home side's best moments throughout with Martial alleged to have been tripped by Idrissa Gueye for a penalty award that saw Jose Mourinho's men take the lead on 27 minutes.
Mourinho said: "The thing I like is the desire to take it". I told the players at half-time it was not a fair result. I think he can.
Martial was excellent in the game as he won us a penalty and scored a brilliant goal to give us a 2-0 lead.