The Football Association have also confirmed the Spaniard will not face disciplinary action over post-match comments in which he claimed Wigan were "robbed" and the performance of an assistant referee was "disgusting".
Relegation-threatened Wigan were beaten 2-1 in a stormy Barclays Premier League clash at Stamford Bridge after Branislav Ivanovic and Juan Mata struck from apparently offside positions.
Martinez spoke to Riley, of the Professional Game Match Officials Board, the day after the game and says he was told the body accepted mistakes were made.
Martinez said: "He just said he understands that at the level of refereeing in this league, they should get that call right.
"I think that is a very honourable way to face mistakes.
"We are all capable of making mistakes and it is about how you react to them."
Martinez was strong in his criticism of the officials, particularly assistant Dave Bryan, after the game but, after speaking to Riley, had not been expecting FA action over his remarks.
He said: "I think they praised me because they were quite surprised I held myself back and I was so respectful."
Bryan was subsequently stood down from tonight's game between Blackburn and Liverpool.
Martinez said: "I think we all know mistakes happen, I am the first one to accept that.
"The problem is when you get two calls in two similar situations, and one of them is so clear, knowing the experience of the linesman - it is really tough to take.
"We are not looking to get people punished - anything retrospective to the event - but unfortunately we were stopped from getting the reward we deserved.
"It is a difficult place to go for a positive result. We need to accept on this occasion we weren't lucky enough to get the result. There were calls you expect to get right at our level."
Wigan, who remain in the bottom three, feel they have been on the wrong end of too many injustices this season.
Blackburn were awarded a goal against them in a 3-3 draw from a corner that was incorrectly taken in November and striker Connor Sammon was wrongly sent off in December's 5-0 loss to Manchester United. The Latics successfully appealed against the Sammon dismissal.
Martinez said: "We have had that sense of injustice too many times this season.
"But you need to look deeper than the results.
"Psychologically a result at Stamford Bridge would have been fantastic but we can still see through it and look at the performance.
"I don't want it to come across that we are blaming the referee for our position - not at all.
"It was just hurtful to be on the back of two decisions at such a crucial time.
"I think it is more important for us to concentrate on the performance.
"If we carry on playing like that in the next six games, I am sure those points and moments of bad luck will turn around and go in our favour."
Wigan face a daunting task as they return to action against Manchester United, the champions and league leaders, at home tomorrow.
The Latics have a poor record against Sir Alex Ferguson's men, having lost all 14 games they have played against them.
Martinez has been on the end of five of those defeats, his side conceding 21 goals in the process.
Martinez said: "The performances we have had at Anfield and Stamford Bridge this season have got rid of that block.
"Against Manchester United you have to be perfect and we know now we can be perfect against these sides. Mentally we are ready for that.
"We have been able to play at a very good standard in the last nine games and that is what pleases me most.
"That shows the group is ready to compete against anyone.
"We are now facing the champions and the team most in form in the league.
"It is a great football occasion for us, that is why we want to be in this league."