Hey, well first of all it's always nice to see someone branching out and experimenting with tactics! It's definitely one of my favourite things when it comes to Football Manager games.
Second, you mentioned you used a high risk attacking style to get back into the game, which is actually a terrible idea. Tempting as I know it is - and I think we've all been there, high risk, direct attacking play is a very ineffective way of breaking down a stubborn defence. By the looks of it your opponent was playing very defensively, with four defenders and three defensive midfielders what that means is a lot of players in the box, crowding out the area, eliminating space and clearing the ball to the three attacking players, who I suspect had free reign behind your midfielders to attack your defense. Urgent, direct play is the worst way to defeat a tightly packed, deep defensive line and in fact you're playing into exactly what they want.
In terms of a strategy to actually overcome such teams, that depends on your players strengths, your preferred style and of course on the opponent you're up against, but there are a few I like to use in particular
1. You could play for set pieces - if you have adept players in this area, good corner takers and taller centrebacks than the opponent for example. It's not guaranteed, but nothing ever is, and at least you can count on the likelihood of getting set pieces. You can't count on the opposition defence making mistakes however. It does require a degree of patience but I'd honestly say it's one of the most reliable methods of pulling one or two back against a stubborn defense and it's saved me a few times.
2. Think about how you're stretching the opposition. They're clearly playing deep, but only have two players on the wing so why not play with inside forwards and aggressive/overlapping wing backs? You might find a quick attack will overload them on the wings and send in a dangerous cross when their defense is unprepared. That all depends on a quick counterattack of course but I find it often does work, even against more defensive teams. You also might find it helps with recycling possession from clearances, stretching out the opposition as they close down the wide players and creating through ball opportunities as a result.
3. You could also try vertical stretching (think false nine dropping deep whilst attacking midfielder or shadow striker rushes forwards) but that may not be the most effective against a team that plays with three DM's and two CB's! It might still help disorient them and pull them out of position as players don't know who to mark or close down so even if you don't see an obvious benefit, it might help upset the opposition and lead through chances in other areas, such as from inside forwards rushing in towards the centre.
4. Long shots! Which feel horribly inaccurate at times, but do actually have their place. Against a team determined to play sitting in their goalkeepers lap, it does make sense to simply give them the box. If they're so focused on defending one area, why walk right into them? Again, you're just playing into their hand so you could just focus on shooting on sight. Like all the above it isn't guaranteed, but there's always the chance it'll go in. It may also create opportunities from rebounds or resulting corners.
That's just a few ideas anyway, you could try one, a few, all, or none of them and find success. The main thing I would recommend against defensive, deep lying teams however is to never play with an attacking mentality, don't push too far forward and don't commit to too fast a tempo unless you have a very organised and prepared defense of your own to cover rapid counter attacks. Just keep the tempo slow, measured, wait for your chances and play in the way that offers you the greatest chance of a reward. You won't always get it, but it's certainly better than giving the opposition what they want.