Ronald Koeman admitted Everton were lucky that Brighton did not score a second goal to clinch victory.
Instead, Wayne Rooney's 90th-minute penalty earned Everton a point.
The relieved Dutchman, who has spent more than £100million in the past two transfer windows, also criticised Dominic Calvert-Lewin and Morgan Schneiderlin for allowing Anthony Knockaert to give Brighton the lead.
He said: 'We had a poor defensive moment, first by Dominic — stay on your feet, don't go down — and the same for Morgan.