Mr Russell offered a full and unreserved apology for giving the wrong information on college funding by mistake last week.
He admitted the error should not have happened. His apology to Holyrood came just five days after First Minister Alex Salmond was also forced to say sorry for quoting the wrong figures on declining college budgets.
Mr Salmond last week told MSPs resource funding for colleges was £545 million in 2011-12 and £546m in 2012-13. But he was forced to explain the figure of £545m for last year did not take into account changes to the bud-get and should have been £555.7m, meaning college spending has fallen more than £9m this year.
Mr Russell said: "Let me make clear again my apology is full and unreserved."
With regard to the incorrect figure, which he had quoted in a letter to an MSP in June, he said: "It should not have happened."
However, Labour education spokesman Hugh Henry, who had raised the issue in the new topical questions slot, hit out at him and said: "There should have been a full statement by Mike Russell. Apologising in this way, I believe, shows contempt for the Scottish Parliament."
Mr Henry went on to accuse the Education Secretary of having misled Parliament on the issue of college funding "not once but twice", adding that the Scottish Ministerial Code states mini-sters should resign if they have knowingly misled Parliament.
He demanded: "Why has Mike Russell not offered his resignation?
"Mike Russell knew in June he had misled this Parliament when he said there is no reduction in funding in 2012-13
"He then knowingly misled Parliament when he said 'I have never said there were no cuts'. He has knowingly misled Parliament not once but twice."
Other MSPs demanded to know why Mr Russell appeared to have been "nodding vigorously" when Mr Salmond quoted the wrong figure during First Minister's Questions last week.
Labour's Neil Bibby said: "Last Thursday, as the First Minister was misleading Parliament at Question Time, television viewers could see Mike Russell nodding vigorously in support of the First Minister's answers. Why was Mike Russell nodding so enthusiastically when he knew the figures being quoted were wrong?"
Mr Russell said he had given the correct figures to Holyrood's Education Committee last month, saying this showed his use of the wrong information previously was a "genuine mistake". He added: "Last week's inaccurate information was based not on an overstatement of spending in 2012-13 but an understatement of spending in 2011-12.
"But let me be clear, even after this additional funding was added in, the revised budget is still falling. I acknowledged this in my evidence to the Education Committee on October 23 and I do so here today."
He also said there would be a full debate in Holyrood tomorrow in which we "will have the opportunity to debate all the issues surrounding college funding" and he hinted there could be more money to come for the sector.
Mr Russell said later: "There remain sums which have not yet been allocated which I would hope to allocate to the college sector, after discussion. I continue to seek in year revisions, as I have always done, in order to make sure as much as possible is spent in the college sector."
Mr Henry added: "It is now clear Mike Russell has knowingly misled Parliament for months. That is a clear breach of the ministerial code which states in these circumstances he should resign. No ifs, no buts, he should quit.
"Mike Russell does not have a shred of credibility left. If he has a scrap of integrity left he will quit."