The point means Ole Gunnar Solskjaer's side remain six points behind Chelsea in the fight for the top four, with Sheffield United moving above us into fifth thanks to their 1-0 win at Crystal Palace.
United now embark on a 16-day hiatus between fixtures, and Shaw was disappointed not to have gone into the winter break on a higher note.
“To be honest I’m really, really disappointed especially with the way the games have been going recently,” the 24-year-old told MUTV.
“We haven’t been picking up too many points and today was massive for us with Chelsea dropping points.