@Hansenhaus You're doing it correctly, but it depends on the difficulty settings. If you needed to push like hell only to keep up with the AI during their mid-race phase (where they're at their slowest), then the setting is probably too high, you'll get swallow up by them during their pushing phase (Opening laps / final lap / in-lap / out-laps)
Tune it down to the point where you can keep pace with those on similar strategy and performance even when managing your car, then you'll be able to counter them nicely on those fast laps without feeling getting eaten up.
At the moment I'm on 90-95 for MyTeam mode, 100 for GP (post v1.08 patch)