In what has been another rollercoaster season for the 26-year-old, Hamilton suffered another dip when he crashed out of Sunday's Belgian Grand Prix, his sixth accident this year.
Trailing championship leader and race winner Sebastian Vettel by 113 points, it is likely Hamilton cannot wait for the season to end, so he has the opportunity to regroup.
Whitmarsh, however, believes Hamilton should not be considering such a position just yet, not with seven grands prix remaining.
"We had a competitive car in Spa, and I hope and believe we will keep working and have that for the next seven races, so there are seven more races to win," said Whitmarsh.
"At the moment he has to put that race behind him and focus on the races in front of us.
"If we look at the next race in Italy, Monza is very different as it requires very low downforce, and so is difficult to predict.
"But there's no reason why we can't be competitive there, and then there are some more typical tracks after that where I hope we can win some of those races."
The title scenario faced by Hamilton, team-mate Jenson Button, who is 110 points down, and McLaren in the championship standings is becoming increasingly difficult.
Asked whether it had now become a case of hope and pray, Whitmarsh replied: "I don't do too much of that myself.
"I try and work on making the car quicker, minimising mistakes, racing well and encouraging the drivers to be good and try and win the next races.
"Generally that's what we've done in this team. I'm sure there are other persuasions in the paddock who have different gods they might want to pray to, but I don't do that."
McLaren have made too many errors this season, on track and on the pit wall, to be truly worthy of either title.
In contrast, Red Bull have been virtually flawless, with Vettel and Mark Webber boasting a phenomenal record of finishing every race this season, and in the top five.
Spa was a perfect case of Red Bull turning the tables on their rivals, scoring a one-two at a track not reputed to be the best for their car.
"We should have been the ones who should have taken the battle to them, but we had our problems that made it a little too easy for them," added Whitmarsh, who then gave credit where it is due.
"I say too easy, but they are doing a good job. They are proving difficult to beat.
"Before Spa they had won one race in the last five, but they keep stacking up the points and doing a good job.
"That is what you have to do if you are going to win a championship."