The Spaniard finished eighth on the stage to La Planche des Belles Filles, one place ahead of an equally opaque Nairo Quintana. He lost 26 seconds to stage winner Fabio Aru (Astana) and six seconds to Chris Froome in the surge to the finish on the 20 per cent finish.
Things could have been far worse after Contador, Quintana and others were dropped by Froome, Porte, Bardet and Martin as they set a furious tempo in pursuit of lone attacker Aru. Fortunately, an easing of the pace and the easier final 500 metres before the kick up to the line allowed them to limit their losses.
Contador is now eighth overall, 52 seconds down on new race leader Froome. He lost 42 seconds to Froome in the opening time trial in Dusseldorf.
"Today the important thing was to save the Tour because I was not great," Contador admitted immediately after the finish.
"It's true that there have been some time differences and that is never good, but we have saved the day more or less and now we have another two days to keep getting ready."
Contador deflected any questions about him struggling to be competitive by suggesting he is playing a long game. He clearly hopes to ride better in the next key mountain stages at the weekend and then in the Pyrenees and Alps in the final week. He also plans to try to take advantage of a possible super team rivalry between Team Sky and BMC.
"I still have to look at the GC carefully but the differences have not been very significant considering how we rode the climb," he said in his defence.
"This is going to be a Tour where consistency is important and I will try to do that. We'll see in the Alps, which are the mountains I like the most, to see if we can try something.
"You never know what can happen. Ask me again in 15 days. What is clear is that there are now very some powerful teams, like BMC and Sky and we will try to take advantage of that."
Contador admitted that he, like Froome, Porte and others, had let Aru slip away when he made his attack because they were focused on watching each other. It proved to be a mistake because Aru gained enough time to move back up the general classification and become a real threat.
Aru is now third overall, 14 seconds down on Froome, with former race leader Geraint Thomas (Sky) now in second at 12 seconds.
"I was more focused on Chris [Froome] and Richie [Porte]. For sure Aru is a very strong rider, too, he already showed it in the Dauphiné, but today I had focused more on watching the other two," Contador said before heading to the Trek-Segafredo bus to warm down and recover for Thursday's sixth stage to Troyes and especially the mountain stages.