RBR chose to sacrifice grid positions in Monza in order to maximise its prospects in the next race at Singapore, where it expects to be more competitive.
“We are for sure going to incur a further penalty,” said Horner.
“I hope we have the choice strategically where we take that penalty, but it is not likely we will get to the end of the year without incurring another penalty.”
Although the prospect of further grid penalties is not ideal for Red Bull, Horner praised the way Renault has responded to its recent run of reliability problems.
After Max Verstappen's retirement from the Belgian GP, Renault has put counter measures in place for issues it has suffered and increased its push for new parts for customer teams, and will assign more personnel to Red Bull from Singapore.
“They have certainly responded, which is encouraging,” said Horner.
“But the problem is, they were new engines in Monza, so if we would have had an issue with the first engine in its cycle it would have been fairly catastrophic.
“The encouraging thing is that they seem to be taking it seriously.
“They are not putting their head in the sand and hopefully that will follow an upward trend between now and the end of the year.”
The Singapore Grand Prix takes place from September 15-17.