Lee Trundle pictured holding the flag bearing anti-Cardiff obscenities

Lee Trundle, 29, and Alan Tate, 23, had been celebrating victory in the Football League Trophy final, at the Millennium Stadium, earlier this month.

Trundle also donned a T-shirt showing a cartoon of a Swansea player urinating on a Cardiff City shirt.

Both men were arrested by police following the game.

South Wales Police said on Thursday a 23-year-old man and a 29-year-old man had received police cautions for public order offences at Llanishen police station in Cardiff.

'Offensive and insulting'

The flag was handed in to police who launched a full investigation following a number of complaints after Swansea's 2-1 victory over Carlisle United on 2 April.

Swansea immediately apologised "for any distress caused" after the incident, saying the players involved had been caught up "in the moment".

A statement on the club's website on Thursday evening said: "Whilst the players concerned may have made a misjudgement on the day, as always stated by the club and players, there was never any intent on the part of the two players to deliberately cause offence.

"The club believes that with their decision not to press charges, the authorities have come to a similar conclusion."

The pair could face possible professional discipline after the Football Association of Wales (FAW) decided charges would be issued against both the club and the two players over the post-match events.

Swansea City spokesman Jonathan Wilsher said the caution represented the end of the police inquiry into the incident but added it had no bearing on the FAW disciplinary hearing.