The gap between City and the continent's best clubs was starkly illustrated on Wednesday as Barcelona dumped the English champions out of the Champions League with a commanding performance at the Nou Camp.
Thanks to the brilliance of Joe Hart, City at least kept the scoreline respectable - losing 1-0 for a 3-1 aggregate defeat - but they were distinctly second best to a Barca side inspired by the magnificent Lionel Messi.
City may have made considerable progress in the seven years since their Abu Dhabi takeover, but the journey still has a long way to go.
Kompany said: "The reality is they were a better team, there is no shame in admitting that
For me there is a big, big difference.
"I will just mention Bayern Munich and Barcelona, and then there are the rest of the teams, with Real Madrid probably in between.
"Ultimately we have always said our goal is to become as good as them, but it will take some time
They are really good.
"Bayern Munich and Barcelona are not just Champions League-winning teams, they are World Cup-winning teams as well
They have generations that have played together a long time.
"Of course we want to make up the gap but you just have to be true to yourself
We have the ambition to be as good as they are one day, but it is not going to happen overnight."
City's exit meant that England will not have a representative in the quarter-finals of the Champions League for the second time in three seasons.
"The gap will eventually get closer," said Kompany.
"Whether it is Arsenal, Chelsea, (Manchester) United, the gap will become closer and I just hope it is us that gets there the first."
City were outplayed in the first leg at the Etihad Stadium three weeks ago but had hoped Hart's late penalty save, which kept the score 2-1, might have proved the tie's turning point.
It proved anything but as Barca dominated from the outset, hitting the post within moments through Neymar
Messi was at his inspirational best, setting up Ivan Rakitic's 31st-minute goal and generally running City ragged.
It was remarkable the scoreline stayed at 1-0, with Luis Suarez also hitting the woodwork twice and England goalkeeper Hart producing a series of stunning saves in one of the best performances of his career.
City might have made the latter stages interesting had Sergio Aguero not had a penalty saved by Marc-Andre ter Stegen but they could complain little about the result.
Asked about Hart's display, centre-back Kompany said: "It was phenomenal
On that side of the pitch I felt we had all the luck we needed to get a result.
"It was probably just the penalty - if we had scored a goal it could have been a different game
It would have been a great way to get back into the tie and it would have been interesting to see what the last 15 minutes would have been like back at 1-1.
"If you want to win against those teams you need a very special performance and a little bit of luck on your side
Then you can beat them, but every team can lose
There is no shame."
Despite progress always seeming unlikely, the defeat is another blow to City's morale after an indifferent spell in the Barclays Premier League.
Having fallen six points behind Chelsea, who have a game in hand, it now seems unlikely City can retain their title and their season is in danger of fizzling out
They could even face a battle to hold onto second place as the likes of Arsenal, Liverpool and Manchester United gear up for a strong finish.
Kompany is determined to ensure that does not happen.
The 28-year-old said: "Forget about Chelsea
We owe it to ourselves, to our fans to have a good end to this campaign
Then again if we finish this campaign as good as we can, maybe there is still something in it
We will have to see.
"It is not in our hands by any means, but we just have to go back and work hard and improve."
Source : PA
Source: PA