The pair were hoping to be part of BT Sport's Europa League coverage, offering insight from the home of the Hoops' rivals with both Old Firm sides in action.
However, the broadcaster saw their request knocked back due to 'security concerns', before both teams stumbled to defeats.
Sutton, an outspoken pundit unafraid to wind up the Rangers faithful, had a pop at Gers on Twitter, while former Celtic boss Lennon is reportedly seeking legal advice.
Ex-striker Sutton said: "I'm not allowed to work on the Celtic game tonight from a studio at Ibrox along with Neil Lennon as Stewart Robertson the Rangers CEO says we are a security risk. Good to see Rangers ground breaking diversity and inclusion campaign 'Everyone Anyone' is working well…"
However, the Scottish champions hit back and insisted they were not in the wrong.
A club spokesperson said: "We have complied with all UEFA contractual obligations to facilitate BT as host broadcaster.
"Any conjecture or speculation is both inaccurate and unhelpful."
Meanwhile, a BT Sport spokesman said: "We had hoped that Darrell Currie and the team would be able to present the coverage of both the Celtic and Rangers UEFA Europa League games live from Ibrox this evening, as we have done in the past.
"Rangers have since raised security concerns and so we have had to change our plans."
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