Kompany was replaced by summer signing Nicolas Otamendi after 75 minutes of City's Champions League opener, with the game finely balanced at 1-1.
Alvaro Morata scored the winner for Juve just six minutes later, but that disappointment looks unlikely to be compounded by a lay-off for their skipper.
Manager Manuel Pellegrini suggested the 29-year-old would be in contention for Saturday's Barclays Premier League meeting with West Ham, and Kompany shares that optimism.
"It was just a precaution," he said
"It is not serious, I know my body."
Defeat to Massimiliano Allegri's side continued a frustrating sequence for City, who have been notoriously slow starters in Europe over recent seasons, albeit against some illustrious opponents.
In 2011 they drew with Napoli, a year later they were beaten by Real Madrid and last term they began with a loss at Bayern Munich.
Only a 3-0 win over Viktoria Plzen two seasons ago bucks the trend but Kompany was not downcast about his team's efforts on Tuesday night.
"It was a very different game than in previous campaigns...there was actually nothing wrong with our performance," he said.
"In that respect I worry a lot less than in previous campaigns
There was no panic and we did not feel we did not know what to do.
"We played against a very good team, last year's finalists, and they did very well.
"We are a little unhappy but we can take confidence to the next game."
City had chances to put the game beyond the visitors, with Raheem Sterling wasting a couple of presentable openings, the first of which arrived in the second minute of the match.
Wilfried Bony also proved a modest deputy for Sergio Aguero, who was only fit enough for a late cameo off the bench.
In the end it was Kompany who forced the breakthrough, pressuring Giorgio Chiellini into an own-goal in a way the Italian was unhappy about.
"Yes, we got chances and we were the better team
We could actually have finished the match much earlier," he said.
"Usually that is not a problem for us but it was this time.
Kompany's injury meant he got to share the field with his Belgium team-mate Kevin De Bruyne for only a few minutes on his home debut, as a 75th replacement for Samir Nasri.
The £55million signing had a quiet time, but his captain believes that was largely down to Juve's methods.
"They scored just before he settled in and then stood with eleven men back, not nine, not 10, but 11 men," said Kompany.
"The Italians are smart
They are a well-disciplined team, they know what to do."
Source : PA
Source: PA