Wing Matt Banahan claimed the headlines with a hat-trick but Meehan was quick to praise the contribution of Barkley - and not just for his 100% kicking record.
"Barkley played well, as he has done since he returned from the World Cup," said Meehan.
"The way he has integrated with the team has improved and the partnership with Butch James has worked to his benefit, perhaps because we've got more threats across the whole team at the moment."
Barkley is one of a number of players out of contract at the end of the season and Meehan added: "We've spoken recently and now it's in the hands of agents and clubs, I certainly hope he will re-sign."
Meehan was broadly satisfied with the performance, saying: "We missed a couple of opportunities in the first half when we kicked the ball away. But we played a little more positively in the first half and it paid off."
Leeds director of rugby Stuart Lancaster was not too downhearted, saying: "Quite a lot of credit must go to Bath, who were exceptional today.
"They are as good a side as we have played all season. They've got pace and power and good footballers who give them width."
Lancaster added: "In a lot of areas, we competed well but we got into a slight catch-up game and, as we tired, they brought on fresh players.
"We came up against a side that is playing really well."