The French midfielder has been criticised for a string of below-par performances for the west London side in recent weeks following his move to the club from Monaco in the summer transfer window.
Bakayoko started for the Blues as Marko Arnautovic netted the eventual winner at the London Stadium with a good finish after just six minutes.
With Chelsea trailing 1-0 at half-time, Antonio Conte opted to replace Bakayoko and bring on Pedro Rodriguez.
The west London side pressed for an equaliser but were unable to find the net as they slumped to a disappointing defeat against their London rivals.
Speaking after Bakayoko was substituted at half-time, Redknapp told Sky Sports: “It strikes me as a tactical move [Pedro coming on for Bakayoko].
“Bakayoko was poor. What Pedro does is given them a bit of pace.”
Redknapp is not the only former player to have been critical of Bakayoko in recent weeks.
On Tuesday night, Chelsea legend Frank Lampard criticised the former Monaco midfielder for “sleeping” in the lead-up to Atletico Madrid’s goal in the 1-1 Champions League draw at Stamford Bridge.
Chelsea, who remain third in the table, must now dust themselves down as they prepare for their trip to Huddersfield Town in the Premier League on Tuesday night.
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