Not true. They make lots of them but they are able to recuperate from that due to their excellent balance (just trying to add to your point, not dismiss it).
As far as PL stats are concerned (per game metrics), United's attacking force that consists of Rashford/Martial/James averages 4.1 losses of possession and 6.8 unsuccessful touches. Liverpool's trident gets dispossessed 4.7 times p/g and has 8.8 unsuccessful touches. As for City, Sterling and Aguero's stats are 3.6 times dispossessed and 3.3 unsuccessful touches p/g. Now, if you consider Bernando as the third player in their 433, their stats are slightly better than ours. If you put Mahrez or Jesus in his place, they are a bit closer to our averages per game. The paradox in all of this is that we're all waiting for a certain Frenchman to come back and add some creativity to our plays while there's absolutely no other creative/attacking player in the top-six rosters who gets dispossessed and has more unsuccessful touches p/g than him. And i don't think we're mad in doing so...
The big difference is that both Liverpool and City have attacking/creative players who can secure and regain possession in the attacking half of the pitch: Second balls, 50-50's, interceptions in the attacking half, all these little details than rarely get mentioned but they are essential for pinning down opponents, sustaining the high-tempo and maintaining players in the final third. Watch any City or Liverpool game, whenever defenders clear the ball there's always a Liverpool or a City player anticipating the second ball. They keep adding pressure not only by playing silky football but by always having bodies contesting every loose ball on the pitch.
This part of the game, the first seconds after an attempt/loss of possession, is something we're really bad at. We press alright, but our press seems to be more similar to Spurs' tactics which aimed to force the opposition to hoof the ball rather than to regain possession high up the pitch and hit the opponent between transitions. One thing i'll agree with you is that you can't teach that to a footballer as it's a natural instinct more than anything else. Herrera had it and that's why we looked more promising when he was in good form. McT has it but his overall game is still very raw. Fred doesn't have it and you can see that he gets bypassed 8/10 times he tries to challenge for the ball. Cutting to the chase, expecting Rashford, Martial and James, Lingard, Pogba, Mata to do it looks like an exercise in futility. And that's one of the reasons i shake my head in disbelief when people vehemently advocate for Mata starting right behind Rashford and Martial.
On the other hand, both Klopp and Guardiola recruit attacking/creative players by looking into this "regaining the ball" category. It's what Wenger neglected with a "true passion" in his latter years and his Arsenal side became the laughing stock of English football. It is also a recurring theme with us. We reach the final third, someone tries to do something, the ball is cleared and we close down the first attacker. Most times we regain possession back in our own half. Rinse and repeat. It makes it very difficult for us to stretch the field vertically. It's not because Martial and Rashford don't look for early runs in behind. We create the spaces, early in transition, but we fail to capitalise on it. And yes, Pogba's passing skills are sorely missed but you can't expect exquisite passes through the lines all the time. KdB is technically as good as it gets, yet half of the chances he creates are the product of him chasing loose balls like a bull in a china shop. Poch based his success not on his players' passing abilities but on the fact that he coached his team to become very "territorial". As for Klopp, there's not a single time when you don't see a scouser being closer to a second ball than his opponent.
It comes as no surprise that whenever the plan is to sit very deep and soak up the pressure to then hit the opposition defenders with pace, we look quite competent. The transitions are lightning quick, passing through the lines comes easier and we can exploit the spaces in behind defences. We don't look like a team that is incapable of playing one-touch football. At all. But when these spaces and the ball are contested, we struggle. And it's easy to say that we need better quality all around the pitch. The truth of the matter is that most successful sides that utilize pressing tactics and want to push their lines higher up the pitch put a lot of emphasis on what happens immediately after the ball is lost and they recruit accordingly.