The Reds edged past Bowyer’s injury-hit side in their sixth round replay at Ewood Park on Wednesday evening.
Blackburn Rovers 0-1 Liverpool
The FA Cup
Sixth Round Proper
7.45pm, Wednesday 8 April 2015
Ewood Park, Blackburn
Winners receive £360,000 from prize fund
Live on BT Sport
And Bowyer now wants to see them lift The Cup in what would be the final game at the club for Reds skipper and Anfield legend Steven Gerrard, should they beat Aston Villa in their semi-final at Wembley later this month.
"I wish Liverpool all the best," said Bowyer, after seeing his team’s run brought to an end by Philippe Coutinho’s second-half strike.
"It would be fitting if they could win it for Steven Gerrard [The Final is on his 35th birthday and would be his last game before departing to Los Angeles Galaxy].
"It would be a great way for him to finish his Liverpool career. He has been one of the best midfielders for some time in this country."
Rovers made Brendan Rodgers’ side work hard to progress, after holding them to a draw in the first tie at Anfield last month and then coming agonisingly close to going the distance in their replay in front of a sold-out Ewood.
"I am hugely proud of the team," he added.
"Not just the team, the whole football club. The supporters were tremendous.
"But there is a hint of disappointment because we have not got through. We have pushed them, [Simon] Mignolet has pulled off several good stops over the two games."