The Spaniard is an admirer of the 25-year-old, having had him on loan at previous club Wigan, and when he became aware of the player's availability he made a last-ditch attempt to snatch him from Aston Villa, where he had already undergone a medical.
An agreement could not be reached, however, and Cleverley ended up back at Villa after they completed an even later loan deal with the paperwork not confirmed until the following day.
Martinez remains philosophical about it though.
"On the last day of the window there are always opportunities that arise and we looked into a couple of those," he said.
"I felt it was an opportunity for us to maybe to add a player that could bring something different but at the end it wasn't right, it didn't work out and I was very pleased this time around we had all the business done well ahead of the transfer deadline.
"We tried to look into a couple of opportunities but they never came off and in reality they probably weren't the right ones for us."
Martinez is happy with the squad he has assembled to challenge on both domestic and European fronts even if he is currently managing a number of injuries.
On a positive note England midfielder Ross Barkley is ahead of schedule on his recovery from a knee injury but will still not be available until mid-October.
"Ross Barkley is progressing well but he is still receiving treatment and he is in week four now," added Martinez.
"He is probably a couple of weeks ahead of where he should be but he is halfway through his recovery period.
"Steven Pienaar, Arouna Kone, Bryan Oviedo and Romelu Lukaku joined the group for training today, which has been very positive.
"But Leon Osman (calf) and Samuel Eto'o (groin) picked up a couple of knocks and we will assess them over the next 48 hours."
Kone has not featured since October but played in a friendly against Stoke this week and is edging closer to a first-team return.
"Arouna played 55 minutes and it was a real positive, exactly the same as Bryan Oviedo (making his comeback from a broken leg)," said Martinez.
"They are on their way back and while it is impossible to give a date I don't think they are very far away."Reuse content