Eden Hazard's 18th goal of the season moved Chelsea 10 points clear at the top of the Premier League as United missed a chance to go above Arsenal into second place.
Chelsea were not at their best, but United failed to capitalise as Wayne Rooney put a great early chance into the side-netting and the recalled Radamel Falcao struck the woodwork late on.
There was drama deep into stoppage-time, when Herrera went down in the area claiming Gary Cahill had upended him, but referee Mike Dean booked the Spain midfielder for simulation.
Van Gaal took great heart from his side's display and appeared to question Dean's decision not to point to the spot right at the death.
He is quoted as saying by BBC Sport: "I am not frustrated, I am proud. Why should I be frustrated? We played the best match of the season.
"In my opinion that is the main decision of the referee [when Herrera was booked]. Maybe you can watch the replays on television."
United remain on course to secure a UEFA Champions League spot with five games remaining, despite seeing their six-game winning league run come to an end in the capital.
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