Despite going behind again when Sturridge struck before half time, Swansea's Bony equalised from the penalty spot.
However, the Swans were unable to recover when Henderson got his second and Liverpool's fourth with 15 minutes left.
"We're unlucky not to get anything against a team at the top of the table and with the games we've had we showed great energy," Monk told BBC Sport.
"The attitude we showed is what we want. I can't complain about the effort and application they put in after so many games."
Swansea are 12th in the Premier League table.