Lukaku, who had endured a quiet game until heading against the post on 79 minutes, made the goal for Martial by heading on David De Gea's long clearance.
But Argentine manager Pochettino refused to cite Kane's absence, through a hamstring injury, as a factor in the loss.
'I think we must keep our identity, our philosophy, it's true that Harry is our main striker, one of the best strikers in the world and anyone would miss what he brings to the team, ' he said in the moments before kick-off.
"But it is not an excuse today". We have to trust in other players. "We'll take the best decision for the team", the 45-year-old stated.
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Speaking at a pre-match news conference, manager Mauricio Pochettino said Wednesday's Champions League meeting with Real Madrid would now be a tentative target for Kane.
"We will see in the next few days if he will be available and fit to play against Real Madrid. They have an advantage of one day's extra rest and time to prepare the game, and we are on the limit".
A hamstring injury kept Kane out of the trip to Old Trafford, with Pochettino selecting Son Heung-min in attack rather than Fernando Llorente. A few games ago, 10 minutes before the end at Huddersfield, it was 4-0 and [we said to Harry] "you must rest because you are going to play two games on global duty". It was a shame to lose. It was the chance for 1-0 up but instead 1-0 down. The effort was fantastic from our players, I feel good, proud of the effort. Pochettino said it was only a "small issue" but he did not want to exacerbate the problem by playing him against United.
"We contained United very well".
"We always believe in the collective, the squad". They didn't create too many chances against us.
Kane was rested for Wednesday's EFL Cup fixture with West Ham United, but Pochettino has revealed that he can not afford to take a risk on the club's top goalscorer after scans confirmed a minor hamstring strain.