The United manager's comments came after another questionable performance from De Gea who reacted too slowly to stop Mason Mount's low drive from beating him for Chelsea's second goal in their 3-0 FA Cup semi-final win.
De Gea allowed Olivier Giroud's shot to trickle over the line in the dying seconds of the first half and moments after the interval Mason Mount's shot evaded his weak attempted save.
The Times described his performance as a "horror show".
Solskjaer conceded De Gea should have saved Mount's goal but stood by the player, who recently surpassed Peter Schmeichel's United appearance record for an overseas player, excluding Irish footballers.