United played with a surprising amount of intensity in the opening 45 minutes in a performance that was a stark contrast to the drab display against Brighton the previous week.
Shaw continued to build on his early season form but apologised to the supporters for the result and felt United deserved something from the game.
“To the fans that came out tonight, we are sorry and we will be better next week, we will improve, we will keep working hard,” Shaw told MUTV.
“We spoke at half-time and Jose [Mourinho] said they hadn't had one corner, one cross or one dangerous opportunity. Then, from their first corner in the second half they had a goal, but even then we should have been relaxed because it was only one goal and we still had a lot of time.
Jose Mourinho consoled Luke Shaw after Manchester United's defeat to Tottenham
(Getty)
Harry Kane's opening goal was followed by a second strike 133 seconds later by Lucas Moura, who was in space on the edge of the box and found the bottom corner with a low shot.
“But then came another mistake, another silly, stupid goal," said Shaw. "We were so on top and it is just really disappointing, everyone in the dressing room is really sad, especially after the first half we had.
“You look at the first half and I think we were outstanding,” he added. We had a lot of chances to put the game to bed. Of the chances we had, [we should have scored] maybe one or two, then for me it would have been game over.
“It is a sad night for us, we have got to pick ourselves back up, keep working hard and we need to pick up points after two losses. We need to win and win in a good way. We played really well in the first half and if we keep playing like that, and take our chances, then we will win games.”
Lucas added a third to seal the result, and after the game Mourinho ended his post-match press conference early as he called for more respect with pressure building after just one win from their opening three games.
Plaguing United’s start have been continuous reports of Paul Pogba and Mourinho’s tense relationship which has prompted Barcelona to explore the possibility of a late transfer.
Mourinho stayed to applaud the United fans after the whistle
(PA)
“You see a lot of things in the media that go on about what our dressing room is like, but we have a really good spirit, a really good group of lads who want to work and achieve big things here,” said Shaw.
“We have a group of hard workers and amazing talents, everywhere you look on the field. We have got to start taking our chances and I am sure we will start winning games.
“It is early in the season, we have got a lot of games to come and we have got to get points. Tonight's result wasn't good enough.
"I am sorry to the fans, not just the ones here but those at home that watched and supported us, but we will look at that over the next week and bounce back against Burnley.”
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