Cleverley, who turns 22 on Friday, received his first call-up to the full England squad this week after impressing in pre-season for Manchester United, including playing a prominent role in their Community Shield triumph over Manchester City.
United boss Sir Alex Ferguson has already identified the young Englishman as a potential homegrown replacement for Paul Scholes, who retired at the end of last term.
Cleverley returned to Old Trafford in May after a season-long loan with Wigan, and Latics boss Martinez had nothing but praise for his former charge.
The Spaniard said: "There's a real satisfaction because he was a really important player for us but it's not a surprise. His talent was quite obvious but he was an example for us in terms of his character, his daily standards and his personality.
"If you ask anyone at Wigan, we knew he was going to have that impact going back to Manchester United. Probably we didn't expect it that quickly and that speaks volumes for how highly he's rated.
"We all wish him well and we'll always remember his best moments with us. He's a special man and without doubt he'll be a special footballer for England."
Cleverley's departure plus the sale of star winger Charles N'Zogbia to Aston Villa has left Wigan potentially light in midfield heading into their Barclays Premier League opener against Norwich on Saturday.
One major positive for Martinez has been the form of 20-year-old winger Victor Moses in pre-season, but the Wigan boss insists the burden must not fall on any one player.
He said: "It is a hole but I think it's an exciting hole, because it means the youngsters that we've got at the football club, who I feel are ready, they've got roles to fill.
"I don't think it's down to one player. It's one of those situations you need to solve as a group of players and I can see that unity and desire to be competitive every week."
After bringing in goalkeeper Ali Al Habsi and midfielder David Jones so far this summer, Martinez is close to tying up a deal for French striker Nouha Dicko.
The 19-year-old is a free agent after cash-strapped Strasbourg were forced to release all their players, but he is unlikely to be available this weekend.
"Nouha has signed. We're just waiting on the paperwork from France," said Martinez.
"He's a really exciting talent. He's a young man, and we want to develop him and try to fulfil his potential, which is huge. Those are the signings that are going to take the club forward.
"It's unfortunate because you don't want to see football clubs going bankrupt but those situations happen. We were quickly aware of his talent and we are delighted that he's chosen us to develop his career."
Martinez has his sights set on bringing in another two players to boost his squad and he played down concerns over the future of striker Hugo Rodallega, who has been linked with a move to Arsenal.
Martinez denied there had been contact from the Gunners, and said: "I don't see it as a negative or a worry, I see it as a compliment. And in the manner the players are working, I've got no worries about that."
Meanwhile, there was encouraging news for Wigan on the fitness of midfielder James McCarthy, who injured his ankle in a tackle from Villarreal's Wakaso Mubarak during last Friday's friendly.
The 20-year-old is unlikely to face Norwich but Martinez admitted he feared it could have been much worse.
He added: "In a way it is positive news because when I saw the challenge I really thought it was a bad injury. As it is the scans were very good and it's only a twisted ankle.
"James is being targeted a little bit too much for my liking, but he's reacted well because that was a really bad challenge. We're delighted in the way he looks after himself."