Yes.
It’s been a while since I’ve played the game, so bear with me: There should be some “tabs” (labeled “1”, “2”, “3”) that appear above that power distribution box. You may have to hover the mouse, or right click it, or something.
Tab number “3” will let you set the power levels to custom settings, instead of the preset ones. Click on tab three. Set your system power levels to whatever suites your style of play. The systems, from left to right in that box, are “weapons”, “shields”, “speed”, “Aux”, at least I think that’s what they are when you select tab 3. You’ll also see “lock” symbols above the columns to keep that column from changing any more as you tinker with the others.
My power preferences on the starter ship were: Set speed to 30 or so, so that I would have “full impulse speed” of about “12” or so. (I have no idea what units that “12” is representing. Quatloos?) Shields at 50. Aux at 40. Remainder in offense/weapons.
But whatever your preferences are, set these settings while puttering around Starbase One, in Sol system, not while under fire. (You can also play with the turn rate/Aux setting in this place, just to see what it will be given a specific setting.) 
Every time you switch ships, you’ll need to reset these settings.
As Apollon said, try to keep firing at the same enemy’s shield facing. This becomes more important, especially when facing “Battleship” and “cruiser” sized enemies at later levels. Hold your torp attacks until you can fire them through downed shields.
I sometimes like to kit out some mine launchers, as well. Tactic: approach enemy, blasting away until I can down one of their shields. Pop a torp through that hole. Drop mines so that they also strike through that hole. Pop evasive maneuver, zoom away to 8-10k klicks away (edge of weapons range), swing around for a rinse/repeat. Not always possible, depending on special abilities of the enemy, but pretty cool early on.
With my setting weapons power levels to 70 or 80, I get shields to drop just a tiny bit faster.
Personally, I also set my camera to “track targeted enemy” instead of “chase” (default). This way, I can see what they are up to, especially if they launch special weapons or trigger a special ability that I need to worry about. You can also see them make course changes, which you may need to adjust to. With camera on “chase”, I found myself merely watching my own cool downs, and not paying attention to what the enemy was doing (and also missed seeing their course changes while out of view, so that they ended up coming back into view at odd or unexpected angles and times).