Gary Hooper's stunning volley deep into first-half injury-time earned Norwich a home point in a game which they perhaps deserved to win, despite going one goal down after Nathan Dyer's early lob.
Hooper's cracker gave Norwich the confidence going into the break, however, and they were unlucky not to capitalise on further chances through Hooper, Nathan Redmond and Michael Turner in the second half as they settled for a point.
While he was pleased to pick up a point after going one goal behind, Hughton was disappointed his side could not grab a winner in the second half.
Speaking to Sky Sports, the Norwich boss said: "On the balance of the play in the second half, against a Swansea team which showed a great quality at times, we were the better side.
"It's a big blow to go 1-0 down, especially with the manner of the goal, but the reaction was very good. We could have and should have gone on and won it."
Hooper's equaliser not only dragged Norwich back onto level terms, but continued the striker's excellent scoring form, with four goals in his last six appearances for the Canaries.
Hughton was full of praise for his goalscorer, saying: "It's a super goal from Gary, and the timing was perfect.
"I think anybody seeing that will agree it's a wonderful strike.
"He's quality, and he's used to scoring goals. What's pleasing is that it's a chance out of nothing.
"When somebody can produce something from nothing, it's clearly special. He has that type of ability."
Hughton was less happy about Swansea's goal, however, with Sebastien Bassong culpable as Dyer capitalised to put the visitors ahead.
"We'll analyse the goal again," Hughton said. "We've seen it, but it's part of the game. You play well, you make mistakes, but it's how you react from that. We reacted very well.
"The second half was good, and we certainly looked to get that winner.
"Our endeavours were all about trying to get that winning goal. You see we're pushing to get the winner. It's a game we don't want to lose on the back of a decent run.
"They broke well at times, but it's important we didn't lose as well."
The point lifts Norwich one place up to 14th in the table after a run of three wins and one draw from their last six games, but, despite a missed opportunity to claim a home win, Hughton was merely happy to keep their run going into the festive fixtures.
"They're all big games for us, irrespective of positions in the table.
"We know where a win would've taken us, but we've kept a run going. We need to keep that resilience and that second-half performance, starting with Sunderland next weekend."