Gerrard came in the second half for Adam Lallana with Liverpool trailing 1-0 at half time, but the Reds skipper lasted for less than a minute, as he was shown the marching orders for a stamp on Ander Herrera.
Former Liverpool player Jamie Carragher has criticised Gerrard blaming it as a moment of madness while Grobbelaar believes the Liverpool skipper is not fully focussed on the task at hand.
Liverpool could have jumped into top four, had they won at Anfield on Sunday, but the defeat leaves them training behind their arch-rivals by five points.
“Steven Gerrard wanted to stamp his authority on to the match,” he told talkSPORT.
“I know that Gerrard’s heart is in Liverpool, and always will be, but his head is in Los Angeles.”
Gerrard will Liverpool after the end of the season and will join MLS club LA Galaxy in the summer.
Liverpool will face Arsenal in their next Premier League game, and should they suffer another defeat, it would probably end all their hopes of making it to the top four.