Paulo Sergio expressed pride in his Hearts players despite their 1-0 defeat by Celtic and urged the club's fans to stick by them in difficult times.
The Edinburgh club are continuing their ban on talking to the media.
But Sergio, after his side missed a late penalty that would have levelled the scores, told his club website: "The supporters can be proud.
"I also beg them to stay behind us and keep supporting the team. It's at times like this that we need their help."
Hearts had gone into the game under a cloud over unpaid wages to their players, with owner Vladimir Romanov having earlier said he is open to selling the Edinburgh club.
However, second-top Celtic relied on a blistering long-range effort from Victor Wanyama after 72 minutes to break the deadlock.
And Eggert Jonsson had his spot kick saved by Celtic goalkeeper Fraser Forster with a few minutes remaining.
"The team was tactically perfect," said Sergio. "We didn't leave any space for Celtic to create chances.
"We were well organised and I thought Celtic were nervous.
"We couldn't do anything about the goal we lost. I can't blame anyone - it was a great goal.
"I just want to say I'm very proud of the boys and of the way they came here and played."
Sergio hopes his side can take heart from their performance in Glasgow and build on that at home to bottom side Dunfermline Athletic next weekend.
"I saw lots of positives," said the Portuguese. "What I ask of the players is that they have that focus and concentration in every game.
"I believe if we do this then we can get the three points next week.
"We have to take the good things from today and keep going. We played a good game."
Sergio ended with a plea to the fans to turn out against the Pars.
"I hope everybody comes to Tynecastle next week," he added.