Everton ended a run of four straight Premier League defeats on Saturday courtesy of Steven Naismith heading home Leighton Baines' free-kick at Goodison Park in the 78th minute, shortly after Fernandinho had put the champions ahead.
Manager Martinez initially appeared frustrated by City's opener, believing Fernandinho to be offside, while Naismith also had a goal disallowed with the score at 0-0.
However, the Spaniard stated that, upon reflection, he felt both decisions were correct.
"Obviously [with] their goal I was disappointed when it happened live, I couldn't see two players behind Joel Robles," said Martinez.
"Looking at it now on the replay the linesman got it right. It was a very good decision, a difficult decision.
"We were unfortunate with the incident that led to the goal with the deflected shot [from David Silva], but the linesman got it right - Seamus Coleman and Mo [Muhamed] Besic played Fernandinho onside.
"We were unfortunate with the action but not the linesman's decision."
Turning his attention to Everton's disallowed goal, Martinez added: "Steven Naismith was just offside and I think it's the right decision."
Martinez, whose side climb a spot to 12th in the Premier League, was particularly pleased with the way his team battled back for the second time a week - after Everton also came from behind to draw 1-1 with West Ham in the FA Cup on Tuesday.
"When City scored we upped the tempo and we looked really strong, threatening, and we defended very well," he added.
"This is a City side playing with confidence, they drag you wide and have awareness of the space.
"The reaction and the character we showed when we 1-0 down was special. It was the same against West Ham. It's a perfect platform to build on in the second half of the season.
"I'm delighted with the reaction, we would have liked the three points but I see a positive performance from our point of view."
