A counter attack is a consequence of winning the ball from the opposition when they are attacking and then converting it into your own quick attack. I underlined the attacking word because counter attacks only happen when the other team is attacking. The attacks that occur from the organized pressing technique that we see nowadays is not always a counter attack as it can happen when the opponent is yet to start a attack (e.g. defenders passing back to another defender who is successfully pressed and a attack starts). Otherwise, the principle of a counter attack and the attacks that happen from pressing high up the pitch is the same, which is to use minimal, quick passes into the final third to score the goal.
Regarding the usage of counter attack, possession based attacks or any other types of attacks, we must understand the player attributes strongly determine the style of attacks. In order to play possession based attacks, you need to have players who can retain possession very well and are very intelligent with the way they create and exploit spaces. During Ole's time, only Matic, Martial, VDB, Mata and Sancho had those attributes with only Matic, Martial and Sancho starting more prominently. Right now, we have Martinez, VDB, Martial, Eriksen and Sancho. Basically we don't have sufficient players who can support possession based attacks. However we have players who are very good with counter attacks due to their attributes supporting direct type of football (quick, tend to dribble to create scoring opportunities and prefer to attack open spaces). That is why we tend to see more counter attacks due to the players not retaining possession properly.
What ETH has done is to use a player very good with retaining and progressing possession in the central midfield, which is Eriksen. All attack and defense movements are influenced by the movement of the central midfield and with a player like Eriksen, the players have more time to position themselves for passes as well as to pass it back to Eriksen if they are unable to progress further. Even when Eriksen is not having the ball, he moves into spaces which can distract the opponents resulting in open spaces for the players to create another passing channel. As a result, we start to see attacks which are more possession based (e.g. the first goal against Arsenal).
In time to come, we will groom or buy players who are capable of retaining and progressing possession intelligently, which will give us more avenue to play possession based attacks. In my opinion, the team must be capable of different type of attacks as we will not always have a perfect squad who can dominate every team. There is nothing wrong with the type of attacks as long as it is able to win you games, as it is always dependent on the type of players who are currently playing. In other words, there is no such thing that a team can only win trophies if they use possession based attacks or they will lose because they are using counter attacks. Its all about what type of players you have and how you position them in a formation so that they can use the best type of attack to score the goals.
