Everton held discussions with United officials on transfer deadline day about a late move for midfielder Cleverley, who spent a season working with Martinez at Wigan in 2010/11.
However, Everton pulled out of a deal when it became apparent United would not sanction a loan move to Goodison and only wanted a £7.5million permanent transfer.
After the move collapsed, Aston Villa - who had also earlier pulled out of a permanent move for Cleverley - agreed a late loan move that was completed only after an extension was approved by the Premier League the following day.
When quizzed about his interest in Cleverley at a news conference on Thursday, Martinez confirmed his interest in signing the player but revealed he was told by United that the player was not available for loan.
This, suggested the Spaniard, could be due to Everton finishing above United in the table last season and thereby posing a threat in their race for a Champions League place this season, unlike Aston Villa who finished in the lower reaches (albeit they have made a fine start this campaign).
"It's the parent club that makes that decision.
"Maybe they just didn't want to send a player on loan to a club that is going to be challenging for things and finished above them last season, I don't know.
"You can look at the table from last season and we finished fifth and they finished a bit lower, so from that respect you can understand.
"But, at the same time, Aston Villa have started the season really well and you look at the performances of Fabian Delph and the young players they have, plus they've got Christian Benteke coming back, they are going to be a strong team.
"But we can't comment on that, it is down to Manchester United. Our information was that the player wasn't available on loan full stop."
Martinez also insisted that the deal did not stall because of any bad blood between the two clubs following the sale of Marouane Fellaini and pursuit of Leighton Baines last summer.
Chairman Bill Kenwright is known as a tough negotiator who fights his corner, but is also well respected among chairman and chief executives across the country.
Kenwright is savvy enough to know that maintaining good relations with rival clubs can only benefit Everton, so he is not one to hold a grudge. And lets face it, why would we be angry at Man Utd for paying £27.5million for Fellaini anyway!?
"I don't think there is any bad feeling between the clubs (following Fellaini and Baines transfer sagas). The chairman has a very good relationship with Manchester United and, as a football club, we are not carrying any sour grapes about anything."
Cleverley's Man Utd contract expires at the end of next season and although the Aston Villa loan deal includes a break clause in January, it doesn't appear to have a permanent option next May.
That would leave Everton open to sign Cleverley on a free transfer, something Martinez isn't ruling out:
"I worked with Tom at Wigan and I am a big admirer of him.
"I will always be interested in Tom in terms of the experiences that I had with him. That will never change. I know the player inside-out but 10 months in football is an eternity. Anything could happen in that time.
We've got two or three young players at Everton who might come through and take their opportunity - Liam Walsh, Ryan Ledson, Kieran Dowell - and they would fit into the squad. It's too early for me to say what we might need in 10 months.
"I know Tom's a very intelligent footballer and I was surprised that a young English footballer had that tactical awareness at such a young age. I feel those kind of players get a lot better as they get older.
"They can experiment with the game in a different way. It's not like they lose their physical capabilities and become worse. Their understanding of the game makes them better. I think Tom is going to be one of the best midfielders in the England camp."