In that time, United have been less successful, winning the league twice and the Europa League once, as well as an FA Cup and a League Cup.
The two sides meet at Old Trafford on Wednesday with City looking to get back on top of the Premier League as they continue to battle Liverpool for the title, while United are hoping to stay in contention for a top-four finish.
Due to the change in the clubs' stature, Silva is confident his side can emerge from the midweek derby with three vital points.
"We had a huge amount of respect for them and I think you could tell," Silva told City's official website.
"Then, after the second year, everything started to change and I think now the respect for us is enormous.
"The [derby] is getting bigger and bigger. These games have something added now, whoever wins will see the effect all around the world. Honestly, the games are getting better by the year, and we hope it keeps going like that.
"The first derbies were complicated, especially in the first year. We drew at home and lost the other one at [Old Trafford].
"But from that point on, everything started to change a little bit and nowadays they have huge respect for us.
"I think that, on balance, the derby lands in our favour. We have won more games.
"There are many memories because we have won a lot of games. I've been lucky enough to score some myself.
"We know the derby is very important for the fans and for us too because when you win this kind of game it gives you a morale boost.
"We need the fans' support, as usual. We know it is a very important game for them and we will try to give everything we have, as we've been doing, and hopefully, we can win the game."
Pep Guardiola's side are two points behind Liverpool but have played a game less heading into Wednesday's clash. City have no room for slip-ups and this is their hardest remaining fixture on paper, with games against Burnley, Leicester City and Brighton to come.