From watching him play last season. I remember him getting caught in possession a few times, and no i'm not going to watch the whole season back just to find those games. It's what I remember. Agree to disagree.
He does get caught in possession at times. It's about average for his position according to statbomb. When you are playing for a top 4 contender in the Premier League you would perhaps want that a little lower. What that doesn´t take into account is the positions it happens in. Allen´s was particularly bad last game as he was the deepest midfielder with the center halves split so it looked a certain goal. Here is a comparison with Emre Can, just to give you an idea how differently they play the midfield role.
As you can see, Allen gets caught with the ball about half as often as Can. Then again Can dribbles twice as often with it so that it to be expected just as I would expect Lallana to get caught on the ball at least twice as often than Allen too. Looking at whoscored.com, below is the number of times a player either is dispossessed(d) or turns-over(t) possession of the ball.
Gerrard 0.5 d / 0.5 t - t+d = 1.0 per game
Henderson 0.7d / 0.8 t - t+d = 1.5 per game
Allen 1.1 d / 1.1 t - t+d = 2.2 per game
Lucas 0.4 d / 0.5 t - t+d = 0.9 per game
Can 1.4 d / 0.8 t - t+d = 2.2 per game*
* - Can´s numbers include his time at fullback. Statsbomb have this split out for just his CM performances in the above radar. Unfortunately I don´t have the means to do likewise.
It you were to plot those on a graph against how often they attempt to beat players with the ball it would pretty much be a perfect correlation between dribbles attempted and how often players lose the ball. So the likes of Coutinho (t+d=2.5) & Sterling (t+d=3.2) have far higher numbers than the likes of Lucas (t+d=0.9. We accept that as that is their role in the side. They also have far more completed dribbles (Sterling 2.8 per game, Coutinho 1.8 p.g. & Lucas 0.2 p.g.)
Similar to Can, we want Allen to do that at the higher end of the pitch and avoid doing so nearer his own goal like at the weekend. It´s one thing losing the ball as a full back in an attacking position or as an attacking midfielder trying to weave into the box. Another entirely to lose it as the last midfielder.