Another miserable afternoon for a Blackburn Rovers side in freefall ended with a fifth successive defeat, three injuries to key players, protests from their travelling supporters and Steve Kean claiming that Gaël Givet, the club's French defender, "wasn't in the right frame of mind" to play. It was that sort of day for the Blackburn manager, who looked on forlornly as his beleaguered players were totally outplayed by a Swansea City side desperate to end their own poor run.

Blackburn remain 19th and only three points adrift but Kean's side have played two more matches than Bolton Wanderers and one more than Wigan Athletic, the two clubs immediately above them. They have four fixtures remaining, including trips to Tottenham Hotspur and Chelsea, and, on this evidence, it is difficult to see them climbing out of the relegation zone.

Against a Swansea team that had also come into this game on the back of four consecutive losses, Blackburn played with an alarming lack of conviction. They looked shaky defensively, were overrun in midfield and, with Yakubu Ayegbeni starting up front on his own, offered little as an attacking force, as Swansea won at a canter. "We want Venky's out", sang the Blackburn supporters, expressing their anger at the club's owners.

To make matters worse for the visitors, Grant Hanley picked up what Kean described as "a really bad ankle injury" which is likely to rule him out for the rest of the season, Yakubu had to be withdrawn because he is suffering from patellar tendinitis and Junior Hoilett was substituted in the second half with a hamstring strain.

And then we come on to the curious case of Givet, who has not played for the club since he was sent off in the 7-1 defeat at Arsenal in February and is reported to be desperate to leave in the summer. Kean said: "It was very apparent when I spoke with Gaël this morning that he wasn't anywhere near in the right frame of mind to start today or be on the bench. I will speak with him again and if he's in a better frame of mind, then great. But today he was nowhere near and that's disappointing.

"I can't get inside somebody's head. I can only tell them how much we need them and how much their team-mates need them and that they need to be like everyone else.

"David Dunn's achilles is screaming, Bradley Orr has taken an injection to play – we need players even if they're injured, even if their heads are not right for whatever reason. We need everyone to be pushing because I believe we need two wins and a draw from our remaining games."

Swansea have no such worries after breaking through the 40-point barrier and climbing to 12th in the table. They quickly imposed their fluid passing game and never looked back from the moment that Gylfi Sigurdsson, who has been a revelation since joining on loan from Hoffenheim in January, scored his seventh goal in 14 appearances with a curling shot that looped over Paul Robinson, Blackburn's best player by a mile.

Nathan Dyer promptly added a second after Danny Graham and Scott Sinclair combined at the end of a move that was reminiscent of the buildup to Alan Shearer's second goal for England against Holland in Euro 96. "That's what it was like, it was great vision," said Brendan Rodgers, the Swansea manager, recalling how Paul Gascoigne and Teddy Sheringham had teed up Shearer in similar fashion.

Dann's own goal, after Sigurdsson's close-range effort had come back off the upright following Sinclair's sparkling run down the left flank, sealed Swansea's win on an afternoon that ended with Rodgers joining his players and the coaching staff in a huddle on the pitch. "It was a symbol of our togetherness," the Swansea manager said. Blackburn should take note.