The Argentinian struck his first goal since his £6million summer move to the DW Stadium to put Latics on course for a place in the Carling Cup quarter-finals.
Boselli opened the scoring in the 51st minute before Ben Watson secured a 2-0 win for the Premier League side with a penalty in injury time.
Martinez said: "You can see Mauro is a really confident finisher.
"A goalscorer in football is expensive and the hardest thing to find.
"He is a real asset to our football club but we need to be patient and fair with him.
"He is coming from a different league, different environment, different culture.
"If you look at the way he has adapted, the work-rate, the way he took the goal, it is very pleasing.
"I am sure Wigan Athletic fans will see the best of him very soon."
Martinez was given a hostile reception throughout the game by Swansea's large away support.
The Spaniard led the Welsh club to promotion to the Championship in 2008 but left in acrimonious circumstances to take over at Wigan last year.
"It is understandable," Martinez said, who once claimed he would only leave Swansea if forced out.
"I heard people say I lied to the fans - I never lied. What I said at the time was because I felt that way.
"After that I was interested in what was best at that moment.
"Right now I think fans will understand why I had to leave at that time and looking at the foundations they have, it has brought them stability.
"I am glad to see a strong side like Swansea City is ready to compete.
"I couldn't lose tonight! At spells I thought it was like watching a game in a foreign country.
"I felt the environment was really electric and typical of two teams wanting to get through to the next round. It was a really high quality game of football.
"If, as a neutral, you don't enjoy that sort of game there is something wrong with you."
Swansea dictated the game for spells, particularly in the first half and were left to rue an early disallowed goal.
Cedric van der Gun had a great opportunity to open the scoring but instead opted to pass across goal to Craig Beattie, who was flagged offside.
Swans manager Brendan Rogers said: "We are obviously disappointed with the goal.
"If you see it again, you will see that it shouldn't have been disallowed.
"It was a wonderful break, the ball has been squared and at the point of contact Craig Beattie is onside.
"Obviously by the time he touches it he is in a forward motion and sweeping it in.
"I'm disappointed with the referee's or the linesman's positioning, but that is how it goes.
"I was very proud of the team. We have come to a Premier League club and shown we can hold our own, if not more than that.
"We created a number of chances. I'm obviously disappointed we couldn't take them but I am very proud of the team and the support we got was phenomenal."