But Italian Costa, who joined Mercedes from Ferrari and led the design of the new W05, does not think the German marque will dominate throughout 2014.
"No, I don't think we can talk about dominance," he told the Italian magazine Autosprint.
"We have seen the progress that Red Bull made between the Bahrain test and the first race -- they were much more competitive than they were in winter testing.
"This gives an indication of how fast progress and the resolution of problems is in formula one," said Costa.
"And it may well be that in a few grands prix many other teams will be at a good level," he added.
Costa, 52, agrees that the performance of the 'power unit' is particularly important in F1's new era, but he doubts that Mercedes is as far ahead of Ferrari and Renault as some currently believe.
Asked if rumours of a 50 horse power advantage for Mercedes make sense, he answered: "No, I don't think they do.
"Let me explain: as teams, we have GPS data, so I think everyone can see that, when it's running at full power, the Renault engine has remarkable performance.
"So probably their deficit at this time is that they cannot maintain this level of performance throughout a race because of temperature, or fatigue.
"But I think that this is a problem that will gradually be solved," Costa added.