The match was overshadowed by the controversial decision of referee Stuart Attwell not to award United a first-half penalty when Callum Hudson-Odoi handled in the area – the official sticking to his decision despite looking at the incident on the pitchside monitor.
While Solskjaer and Luke Shaw vented their anger at the situation in post-match interviews, the manager's news conference eventually turned to the other major talking point; United's inability to score against the league's better teams.
"We're not scoring enough goals, that's for sure," Solskjaer told reporters.
He is not wrong – the draw at Stamford Bridge was the fourth successive 0-0 draw United have played out against other "big six" opposition, while they have not scored in any of their past six meetings with teams of this calibre.