Potter stepped into the Stamford Bridge hot seat last week after Thomas Tuchel was sacked following the club’s shock defeat away to Dinamo Zagreb.
The former Brighton head coach was frustrated with the result but praised the attitude and application of his players.
“They gave everything,” he said. “We’ve only got one point so we’re disappointed with that but I was very proud of how they acted today.
“It’s not been easy for them either. The change of coach and all that comes with that, but their response has been brilliant.
“They’ve acted really, really well, professional, honest, responsible, so from an effort perspective it was absolutely 100 per cent there.
“They’re top players, they’re working hard for each other, there’s a nice spirit in the group. They’re disappointed because the results haven’t gone as well as they would like, which is normal and you can feel that disappointment, that frustration.
“But it’s my job to try and help them get the results they want, that we all want. Today’s not the best start in terms of points for us but in terms of how we acted on the pitch as a group, lots of positives.”
Chelsea were back in action after the Premier League’s weekend hiatus due to the Queen’s death.
But they could not atone for last week’s 1-0 loss in the Croatian capital, with substitute Hakim Ziyech wasting their best chances after Silva’s costly lunge was punished by the Austrian champions.
The Blues – two-time winners of the competition – face back-to-back group stage meetings with AC Milan early next month.
Potter remains confident of prolonging the club’s European campaign into the knockout stages.
“We can’t lie, it’s not the position we want to be in but we have to respond,” he said. “It’s as simple as that.
“It’s going to be a tough group. But there’s enough quality in the team, enough quality in the squad that we can respond and we have to look forward to those games.”
Salzburg, who enjoyed just 28 per cent possession in west London, sit a point above their hosts having drawn 1-1 with Milan last week.
Head coach Matthias Jaissle said: “We are very proud of the team. It’s something special to get a point here at Stamford Bridge.
“We’re the youngest team in the Champions League competition, so everything is very positive.
“Everyone gave their all, we had the right fight mode on the pitch so that’s why we deserved this point.