Ralf Rangnick's side took a first-half lead but crumbled in the second-half for the third match in succession after a dominant start to the match at Old Trafford.
"History is repeating itself again," Shaw told Match of the Day. "We started really well the first 20 minutes, got the goal and it just happened again. We know it's not good enough and it needs to change quickly.
"If we take our chances early in the game it's a different story. We know we need to get better. We can't over-think it. We want to get in the Champions League and it's not good enough and there's no way we will get in Champions League if we keep dropping points.
"The most important thing at the moment is results. It's about picking up the points and we need to be climbing the table."