Skipper Leon Britton was left frustrated Swansea were not able to take advantage of Valencia's indifferent recent form to book their place in the last 32 of the Europa League - but insisted "it's still in our hands".
Swansea would have guaranteed their berth in the next phase with just a draw against Valencia at the Liberty Stadium but they slipped to a 1-0 defeat following a 21st-minute goal from Dani Parejo.
With Valencia having only won three of their previous nine matches in all competitions, losing four, Britton had high hopes for this match but he conceded the Swans were below par on the night.
He told ITV4: "We weren't at our best tonight, our passing wasn't great, but you've got to give them credit as well. They didn't let us get into our rhythm.
"They're a good side, they're a team with a lot of Champions League experience, but they are in a bit of a difficult time so we're disappointed we didn't capitalise on that."
Michael Laudrup's men thought they had equalised through Alvaro Vazquez just before half-time but his effort was ruled out for offside.
Midfielder Britton said of that: "We got told as we came in at half-time that it was onside, so it's frustrating. The officials have a difficult job but at the same time it's very frustrating.
"But it's not all doom and gloom, we've still got the opportunity when we go to Switzerland. It's still in our hands.
"Obviously we wanted to do the job tonight in front of our fans, but we have to do it the difficult way now. Every game's a learning experience."
The defeat to Valencia, who registered the only goal through Daniel Parejo after a deflected Juan Bernat strike fell to him in the box, means Swansea's quest to secure a place in the knockout stages of the competition will go down to the wire.
A point would have been enough to send Swansea through with a game to spare, but instead they must wait until their final game against St Gallen to decide their fate.
Laudrup's side are three points clear of third-placed Kuban Krasnodar, with the Russians having to go to group winners Los Che in the final round and Swansea three goals better off.
But Swansea would have secured the draw they needed had the Italian officials not made a major error just moments after Alvaro Vazquez had replaced Bony.
The Spaniard netted from close-range after Valencia keeper Diego Alves had parried Jonjo Shelvey's volley from an Angel Rangel cross.
However, the assistant referee raised his flag to the fury of the home players, with replays showing Shelvey and Vazques were onside.
It would have done little for Laudrup's mood, with the Dane still nursing a grievance over the late penalty his side conceded in the recent 3-3 draw with Stoke.
"I have watched it a few times," he said. "When Shelvey is going he keeps his flag down, it is when Alvaro scores he puts it up, but he is at least a yard onside."
He ruefully added: "I can't really talk about referees."
But Laudrup insisted he was not concerned that his side's bid for the knockout stages has gone down to the last game, having opened this Group A campaign with a famous 3-0 win at the Mestalla.
"I know in European competition you have to play until the last game and I knew from the beginning that it would be very difficult," he said.
"Today we saw a Kuban side who everyone thought was the weakest in the group win 4-0 at home against St Gallen.
"It is not easy and you have to play until the last game.
"Tonight I think Valencia were the better team in the first half and dominated in midfield, not that they created many chances.
"We had a disallowed goal but Alvaro was at least one yard onside.
"In the second half we took over and had three or four chances but had one saved on the line and couple of others that very close.
"Maybe we will have to get that last point in Switzerland."
Valencia coach Miroslav Djukic was pleased to pick up a positive result after an unsettling few days following the appointment of sporting director Francisco Rufete and the new man's decision to start recording the Serbian's training sessions.
He said: "We are very happy especially in this situation. We needed a win to get our confidence back
"We need to learn how to suffer in games, we played a very good team who came at us in the second half and we coped well.
"I am very happy for the players and everyone at the club."
He added: "I think Swansea are a great team and will qualify, from the start of the group I thought Valencia and Swansea would qualify."