"These first races have been a complete nightmare," Newey told reporters after first practice at the Hungaroring saw Alonso lap 13th fastest, an improvement on being near the back of the field.
"Hopefully we can get at least to a point of respectability now and then from there we can try to keep moving forward."
Silverstone-based Aston Martin have scored one point in 10 rounds and are last but one in the standings, with only newcomers Cadillac behind them.
The one point also fell into their lap after Cadillac's Sergio Perez, who had finished 10th in Monaco, was penalised for positioning his car wrongly at a re-start.
Newey was reluctant to set any performance targets for the weekend or the second half of the season.
"I've never been a fan of setting goals," he said.
"I'm much more of a fan of working logically through problems, getting everybody working together, getting the culture together."
Newey said Alonso was an amazing driver who brought a huge amount to the team in feedback and ability.
"So for us of course it's important," he said when asked how much of a priority it was for Alonso to stay.
"I'm pretty confident that Fernando is enjoying his time with us and that we will continue our relationship."
Newey said the relationship with Honda, whose engine has been the least competitive of those on the grid in the first year of the partnership, was improving all the time.
"Out of what can only be called a disastrous start, the positive of that... is it's brought Honda and ourselves into a very close working relationship," he said.
"And we continue to develop that in all areas. So I think I'm very happy with the progress we're making from a relationship point of view, And normally relationships improve and performance also improves."
