The 23-year-old failed to get on the score-sheet in a 4-1 victory over the Blues on Tuesday night but Chelsea captain John Terry struggled to contain the former Magpies forward.
Johnson believes Carroll, who netted in last weekend’s FA Cup final, has earned his place in Hodgson’s squad after his performances over the last six weeks.
“Should he go? Yes, definitely,” Johnson told Liverpool’s website.
“In the last few weeks Andy has been fantastic for us – he has been unplayable.
“Chelsea have got two big centre-halves and he just threw them around. He looks like he’s quicker and he’s working a lot harder. He’s doing really well.
“John Terry looked petrified at times.
“Andy is a big lump but he’s good on the ball and works really hard. He will scare a lot of defenders.”
Carroll sealed a £35m move from Newcastle United to Anfield in January 2011 – a record fee for a British player – but has struggled to make a telling impact on Merseyside.
However, the England international has finally started to show signs of improvement under Kenny Dalglish, with a return of three goals in his last six appearances.
His display against Chelsea on Wednesday night also drew praise from fellow England international Wayne Rooney.
The Manchester United striker Tweeted: “Andy Carroll was unplayable tonight.”
Hodgson will name is 23-man squad for the tournament in Poland and Ukraine next Wednesday.
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