The under-pressure Toffees boss thought his side controlled the first half of their latest Premier League defeat.
Martinez said after the game, which Everton lost 1-0 courtesy of Anthony Martial's winner, that he was happy with his side's first-half performance and suggested they had been in full control at Old Trafford.
"First half, probably exactly what we were looking for," he explained. "That is the first time I’ve seen such a controlling 45 minutes."
But Kilbane, who spent three years at Goodison Park in the mid-2000s, had a different take on proceedings.
"I’m sorry, I can’t agree with that at all," the 39-year-old told Match of the Day 2. "I think Everton today were very poor, particularly in possession of the ball I felt during the first half.
"The quality they’ve got in that squad… they’re twelfth in the Premier League this season and they’re under-performing, seriously under-performing.
"Time and time again today it was either the wrong decision or poor quality. For all that Roberto Martinez spoke of controlling the tempo of the game, they didn’t create any chances."
Despite a squad comprising the Premier League's third highest scorer in Romelu Lukaku and England internationals John Stones, Ross Barkley and Phil Jagielka, Everton have disappointed this season and look set for a second successive bottom-half finish.
The Merseyside club are currently six points behind 10th-placed Chelsea, though they have a game in hand on both the Blues and West Bromwich Albion.
The Toffees will compete in their second domestic cup semi-final of the campaign later this month, but supporter patience in Martinez is rapidly wearing thin.
And many of them took to Twitter after the game to call for his sacking.