The Swans had looked set to back up their stunning 3-2 success over Arsenal by claiming another of the Premier League's major scalps as they led Chelsea deep into stoppage time.
Scott Sinclair had given the home side the lead by scoring a stunning left-footed volley against his former club, which he marked with a restrained celebration.
But the Welsh club were struck a cruel blow when Jose Bosingwa's driven ball across the face of goal took a wicked deflection off Neil Taylor to deceive goalkeeper Michel Vorm and end up in the back of the Swansea net.
The disappointment was clear to see on the faces of several Swansea players at the final whistle, perhaps deepened by the fact that they had come within an ace of beating the London club despite turning in one of their less impressive home displays.
The Swans were uncharacteristically sloppy in possession as Chelsea pressed high up the field in the second half, leading to a sustained siege on the home goal which they grittily weathered until the dying seconds.
But Rodgers has told his players that the hurt they felt is a positive sign for the club's future as they continue to win plaudits during their maiden Premier League campaign.
He said: "We were so dominant in the first half even though we didn't pass so well in the second half.
"When we had the ball we gave it away far too cheaply and probably invited pressure on us, but I still felt comfortable, we restricted them and it was a case of seeing it through and unfortunately we didn't do that.
"Big clubs will feel they should beat teams like Swansea and we are disappointed but there is nothing but credit to us.
"That's the third big club in a row to come here after Tottenham and Arsenal and we have had a win and two draws.
"We are developing all the time. To walk off disappointed that we didn't win tells us a big story about how we are developing."
The result continues Swansea's record of being one of only two clubs in the division, along with leaders Manchester City, not to lose back-to-back league games so far this term.
And Rodgers, who strengthened his squad with the addition of Wrexham full-back Curtis Obeng on transfer deadline day, hopes his side's proven ability to bounce back after a disappointment will be on show again when they face West Brom at The Hawthorns this weekend.
He said: "We have never lost two in a row at this level, only City and ourselves have managed that this season, which tells you something about our mentality and I am optimistic and positive.
"There are areas we can improve but you can't dwell on it and we will be motivated to put it right at West Brom.
"We are not going to get hung up about it. We will go and play our game."
For Chelsea manager Andre Villas-Boas the result threw up further headaches for the Portuguese to deal with.
Ashley Cole's late sending-off after receiving a second yellow card will rule him out of Sunday's clash with Manchester United, while Fernando Torres' latest goal drought extended beyond the 1,000-minute mark.
But Villas-Boas, whose side are now seven points behind third-placed Tottenham, still has confidence in his Spanish striker's form, despite him marking the anniversary of his £50million move from Liverpool with another unimpressive display.
He said: "It is normal, he is taking his time.
"The confidence is there and we believe a lot in the player, he helped the team with his lay-offs and passing. If we need to create more opportunities for him to score then that's what we need to do."
Villas-Boas admitted that his side could not be counted as title contenders after dropping another two points.
Goalkeeper Petr Cech agreed with his manager's assessment.
Cech told his official website: "We don't have to mention the word 'title' because the Manchester clubs will not drop many points. That's the reality.
"I still think it is realistic to target the third spot but to do that we will need to succeed in Sunday's match (against Manchester United)."
