Schumacher started well, moving from 11th to 8th on the opening lap, but wound up ninth behind his Mercedes team-mate and fellow German Nico Rosberg who was eighth.
To make matters worse, the seven-time champion was lapped by rivals Spaniard Fernando Alonso and Brazilian Felipe Massa of Ferrari, and German Sebastian Vettel of Red Bull.
The 41-year-old was pleased with his start but admitted that there was no way of keeping up with the front-runners.
“I had a pretty good start today but from then onwards, there was not much more that we could do,” he said.
“We changed the strategy to react to the circumstances and maybe I could have finished slightly higher, but in the end that would not have changed much in a race where we had hoped to be more competitive.”
“What we achieved after my stop was the maximum that was possible. Of course I would have wished for more, especially as our race performance tends to be better than qualifying, but it did not work out.”
In spite of his result, Schumacher added that there is no need for drastic measures.
“We will certainly not get nervous but we have to sit down, analyse the reasons and put the right solutions in place.”
Rosberg, 25, also felt he got the most out of his car and complimented his team on their impressive pit stop performance.
“My strategy was good and the guys made a fantastic effort with my pit stop being the quickest of the race.” said Rosberg
Having finished third at Silverstone two weeks ago, Rosberg admitted he was frustrated and is hoping for a better performance in Hungary.
“We made the best of our situation today but it is frustrating after being on the podium at the last race. Achieving eighth place is damage limitation really and we were able to minimise the loss to Robert in terms of points but it has generally been a struggle this weekend.”
“There are surely better times ahead in Hungary.”