As Archbishop of York, the 71-year-old would normally have been granted a life peerage to continue sitting in the House of Lords after his retirement in June.
According to the Sunday Times, Downing Street has broken precedent by failing to announce his peerage, with the Government seeking to excuse the move by saying it needs to slim down the Upper House.
Stephen Cottrell, who will today be enthroned as the 98th Archbishop of York, is among those to have expressed his disappointment.
"Disturbed to find out today that whether it be through negligence or intent my predecessor Sentamu has not been given the peerage that has been the custom for many years," he said.
"I trust this will soon be rectified. The House of Lords will benefit from his voice."
Lord Richard Newby, the Leader of the Liberal Democrats in the House of Lords, who lives in Ripon, also expressed his dismay on Twitter.
"For Downing Street to claim that John Sentamu didn’t get a Peerage because the Lords was too large is an insult and a disgrace," he said.
"They are stuffing the place with people who don’t deserve to stand in Sentamu’s shadow."
Labour's David Lammy MP, Shadow Lord Chancellor and Shadow Secretary of State for Justice, dismissed the move as "blatant institutional prejudice".
Tradition suggests the former archbishop should have been given the peerage to enable him to continue sitting in the Lords in a personal capacity, rather than as lords spiritual.
His predecessor Lord Hope and the former Archbishop of Canterbury Rowan Williams are among those who have previously been recognised.
According to the Sunday Times Sentamu was informed on June 26, more than a fortnight after his retirement, that he was in line for a peerage and asked to confirm his willingness to accept.
Instead of a formal letter confirming that his name would be among the 36 appointments on July 31, the paper reports that he received a phone message through intermediaries, telling him he had missed out and would have to wait until the next round.
Among those made life peers in July were former Brexit Party MEP Claire Fox and Boris Johnson's brother Jo Johnson, a former MP. There were no new peers from the black community.
In a statement to the Sunday Times, the Government said: “The size of the House of Lords needs addressing. But given retirements and other departures, some new members are needed to ensure that the Lords has the appropriate expertise and it continues to fulfil its role in scrutinising and revising legislation.”