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On his 100th start as Chelsea captain, Cesar Azpilicueta opened the scoring for the Blues in the 10th minute, before an overhead kick from Alireza Jahanbakhsh levelled the game six minutes from time.
Both sides managed just five shots on target from their 16 each, but it was an opportunity missed for Chelsea boss Lampard, who felt his side should have capitalised on the chance to cement a place in the top four.
"It was frustrating for different reasons." Lampard told BT Sport after the game.
"In the first half, the game was there to be won. We weren't ruthless enough. We got the goal and we had the possession. But we just didn't kill the game off.
"We allowed them to stay in the game. In the end it was a wonder goal but we were lucky not to lose the game.
"In the end, the tactics matched up for both teams but they were better than us. We have to take that on the chin."
Chelsea sit fourth in the table on 36 points, five ahead of Manchester United who have the chance to close the gap when they take on Arsenal in the late kick-off on New Year's Day.
The Blues have now won just twice in their last six league games, losing three and drawing one. They've beaten London rivals Tottenham and Arsenal, but have lost out to three sides in the bottom half of the table in Everton, Bournemouth and Southampton.
The draw with Brighton, who are also in the bottom half, proved just how inconsistent Chelsea have been this season, an issue which their manager wants to resolve as soon as possible.
"[The lack of consistency] is a concern," Lampard added. "It's something we absolutely have to look at.
"We have to look at the game today. It's a point, I'm not happy with the performance."
Chelsea's next two league games involve meetings with Burnley and Newcastle, before a tricky run of fixtures against Arsenal, Leicester, Man Utd and Tottenham.