England ended a demoralising run of seven defeats when they beat South Africa 23-21 at Twickenham.
But Johnson, who skippered England to World Cup glory three years ago, believes replacing Robinson would make a difference to the faltering world champions.
"There are many reasons England are in the mess they're in but the buck has to stop with the head coach," Johnson told the Mail on Sunday.
"He had made some very poor selections and decisions before and during games. Ultimately it's his responsibility.
"Would it be a knee-jerk reaction to sack Robbo? Let's be honest we're not talking two defeats here, we're talking seven.
"So if you ask me if replacing the head coach at this stage - with 10 months to go before the World Cup - will make a difference, my honest answer is 'yes'."