Wales was around 40th out of 68 in the last Pisa international school test results for science, maths and reading released last December.
Wales also fell behind the rest of the UK with an average score of 468.
Mr Lewis has set a new target score of 500. Conservatives said that amounted to "stagnation" not "aspiration".
As a comparison, Scotland scored over 500 points last year, which means that the new target for Wales in 2021 would put it on a par with Scotland in 2013.
Mr Lewis had told BBC Wales last December that ditching the target was the easy way out and he did not want to lower pupils' ambitions.
On Thursday he insisted the new approach was still ambitious.
"This is a better target, I think, because it relates to what teachers can aim for in their classrooms, in their schools, as regards the actual progress of young people," he said.
"If we say to a head teacher 'we need to be in the top 20', it's very difficult to translate that into how their 15-year-olds should do at GCSE.
"But if we say 'score 500' they can measure their progress towards it."
Conservative shadow education minister Angela Burns ridiculed Labour for seeking to "raise Welsh performance from the worst performing UK nation to the second worst by 2021".
"This isn't aspiration, but stagnation," she said.
"This feeble new target shows a poverty of ambition for young people."
But the National Union of Teachers (NUT) said it was "pleased" the minister was taking the "sensible approach".
Owen Hathway, of NUT Wales, said: "It was always a little unwise to have created such targets simply for the headlines they drew.
"Evaluating the progress of the points scored is a far better and more productive way of measuring progress."
Plaid Cymru education spokesman Simon Thomas said he was "glad" Mr Lewis had now "placed more realistic expectations on the teaching profession".
However Aled Roberts, who speaks for the Liberal Democrats on education, called on ministers to "make up their minds once and for all about their education strategy or hold up their hands up and admit they don't know how to fix our education system".
The new target was announced as part of an education improvement plan launched by Mr Lewis.
Qualified for Life sets out the Welsh government's vision for education up to 2020, with the ambition that every learner in Wales should benefit from "excellent teaching and learning".
An annual "report card" will show how Welsh education performs against a range of measurable targets.
The target to put Wales into the top 20 best-performing countries in education by next year has been scrapped by Education Minister Huw Lewis.