Former England and British & Irish Lions coach Clive Woodward says the tourists should have dispatched the Springboks in the final Test in Cape Town over the weekend.
The Boks overturned a 10-6 half-time deficit to win 19-16 and claim a 2-1 series victory.
Woodward, who earlier hit out at SA Rugby's director of rugby Rassie Erasmus' role as a "water boy" and his criticism of the refereeing during the series, said the Lions "blew it" and had "only themselves to blame".
In last Saturday's final Test at Cape Town Stadium, the Lions turned down several kickable penalties and in the end it proved costly.
"This was a game and series the Lions should have won. All week (head coach) Warren Gatland spoke of the game as a cup final, which was exactly the right mindset, but come the day the Lions forgot that maxim in the heat of battle," Woodward wrote in a column for the Daily Mail.
"When the Lions were dominating the game in the first half, they moved away from that ruthless mindset. I am not talking about the try-scoring pass that Liam Williams should have made to Josh Adams, which cost the Lions so dear, but the decision to twice spurn very kickable penalties and go to the corner instead."
The Lions went 10-3 up in the first half when hooker Ken Owens scored after a lineout drive. It came after they also opted against kicking for goal.
But Woodward feels after that they should have built on their lead by kicking penalties.
"(Captain) Alun Wyn Jones's decision has been described as brave but I'm not sure. Although you want tries when you can get them, the priority is to take every point on offer. Building the score is vital, yet the Lions turned their back on six points there. A half-time score of 16-6 would have given them more breathing space," he wrote.
"Of course the decision was nuanced, I understand that. Earlier, the Lions had opted for the corner and Ken Owens had scored, but having got that try and put a little daylight between them and the opposition, surely the best option was to build the lead.
"That period of the game when the Lions blew the Adams 'try' and turned down two shots at goal will haunt their players and fans alike. They should have gone down the tunnel 21-6 up, possibly 23-6 up if the Adams 'try' had been converted."