Chelsea, beaten in the Premier League by Everton on Saturday, looked short of ideas all night in a stuttering display, though they led 1-0 following a neat finish by Oscar just before halftime.
The Brazilian hit the bar soon after the restart as Chelsea briefly turned on the style but they were never able to take complete control and Mohamed Salah equalised in the 71st minute.
Swiss champions Basel, beaten by Chelsea in the Europa League semi-finals last season, grew in confidence and completed their smash and grab raid nine minutes from time when captain and centre forward Marco Streller cleverly glanced in a near-post header from a corner.
It was Chelsea’s first home defeat in the Champions League group stage in 30 matches, dating back to a 2-0 loss to Besiktas in October 2003.
“We wanted to win of course but we have to respect a team who showed they have quality and experience,” Mourinho told reporters.
“Basel played very well. We had a lot of the ball but we couldn’t create many chances. In the end we lost three points, we must get them back somewhere.
“Normally you have to win at home and get a few points away Now we must win remaining home games against Schalke and Steaua Bucharest and will probably we will have to go away and win at Basel.”
That could be easier said than done as the team who have won the Swiss title four years in a row played with growing confidence and no little skill.
They were on the back foot for much of the first half as Chelsea gave a debut to 30 million-pound ($47.9 million) signing Willian and a first home start for 20-year-old Marco van Ginkel but although the Londoners dominated possession they were pedestrian and disjointed for most of the first half.
A neat pass by the ever-aware Frank Lampard enabled Oscar to give them a flattering halftime lead and their formidable home record in the competition looked safe.
But Basel, who took four points off Manchester United in the Champions League in the 2011-12 season, were always in the game and having survived Chelsea’s best spell it was no real surprise when they levelled after impressive Egyptian Salah played a nice one-two with Streller and curled in a confident low shot.
They went close again through Streller but Chelsea failed to heed the warning and the big forward got in front of Gary Cahill to head the winner nine minutes from time.
Chelsea, European champions in 2012, drew their first home Champions League game last season, 2-2 with Juventus, to set the tone for a scrappy campaign in which they failed to progress to the knockout stage.
“We go home sad, the supporters go home sad but tomorrow we wake up and go training and prepare for the next match,” Mourinho said.
“The only way is to believe in each other stick together and try to get the result against Fulham at the weekend to bring a smile and then try to recover these points we lost today in the next match in the Champions League.”
Basel coach Murat Yakin was delighted to take such a prestigious scalp.
“It’s a great honour for us to win here,” he said. “But we gained a lot of experience from last season’s games (in the Europa League) and we didn’t come here to hide.
“We had to defend a lot in the first half, we were probably too defensive, but we attacked a lot more in the second half and I always felt we looked dangerous.”
(Editing by Ed Osmond)