I don't use counter press ever, so I can't comment. I would imagine it entirely depends on just how you're setting up though. Don't just change that one instruction.
Here's an example of what I do. I've managed a few teams in my career and every time, I set up tactics for them. I've had 424s, 352s, 4231s, 442s and 442 diamonds so far. At my current club, I've now changed to a 4132 for the last 2 seasons (I've managed them for 5) as it matched the current squad better.
Here's my normal tactic that I will use in 95% of my matches:
This is a creative and technical team who can rip apart most teams I face.
If I want to see the game out or I have a tough match coming up that I am not confident in, I'll swap to this, though it has been modified a couple of times and I'm still not very happy with it:
The shape is similar, but one fullback is more defensive and won't take part too much in transitions and attacks. It's a 4 man team that watches a quick attacking opposition. The other fullback bombs forward as there should be space to push into aggressively.
The key is that I have a much more defensive set of players here. Pedro is a centreback/fullback hybrid and so is Janssen. Gavrilovic is a tank at DM. The other three midfielders (two of them shifted into new positions) are all defensively solid with Strength and Tackling above 13 and that includes the CM/A.
The CM/A is probably the biggest change. I switch from a 8 Tackling, 9 Positioning, 7 Aggression and 12 Strength player to someone with 13, 14, 10 and 13 for those same attributes. Next season, I am going to use Bossard there (who you can see can even play as a striker) and he has 12 Tackling, 10 Positioning, 20 Aggression, 19 Bravery, 17 Anticipation and 13 Strength. He's also a decent finisher, so he can do it all, really.
The DLF is also different. Yates is faster than Esposito and a better finisher with fantastic Anticipation, something that is useful on the counter.
Obviously you can sub this many player within a game, which is when I use this the most, just to see out the last 15 mins. I tend to sub on the more defensive left back (as he's a lot better and bigger from a defensive point of view) and the CM/A spot. I usually just have 2 subs left by that time.
It's just an example of what I change and it's not always the same things. Sometimes I drop the LoE too or I'll drop to Balanced Mentality. I also only do it if a fear their attack will overpower my original tactic, which is not that often.
You can argue that I got lucky, but being 1-0 up from the first leg, I used this in the second (away) leg against a very strong (better than mine) Juve team and I scraped by. I created the only CCC, restricted them to poor chances on the whole and a lot of off target shots.
As you can see from who scored and assisted, they're not my usual starters either, so we were a little under strength but this was a cup match.