The Lake County couldn't close the gap in time against the Tribesmen.
Westmeath Manager Mark McHugh says his players "can't feel sorry for themselves" following defeat to Galway yesterday.
The Lake County suffered a 3-21 to 2-21 defeat on the road, with the Tribesmen securing their place in the quarter-finals.
Despite being nine points down inside the final 10 minutes, Westmeath closed the gap to two points thanks to a Jack Duncan goal and two pointers from Robert Forde and Sam McCartan.
However, Shane McGrath's fisted effort was enough for Padraig Joyce's side to seal victory.
McHugh's side turn their attention to a clash at home/away to xx this weekend.
He says the panel will learn from this experience:
Mark McHugh spoke to the media, including Midlands 103 commentator Gerry Russell following yesterday's game in Salthill:
Our coverage of the game is with thanks to Total Tile & Bathroom Centre Mullingar.
Top quality products and service. Call to their newly renovated Showroom
Or visit them on Instagram & Facebook.
Full Interview: Portarlington Footballer Ronan Coffey
Full Interview: The Down's Manager Dermot Power
St Brigid's And St Joseph's Aiming To Reach Leinster Semi-Finals
Ballinagar And Milltown To Meet In Leinster Intermediate Quarter-Final
Ronan Coffey Praises Portarlington’s Young Guns Ahead Of Leinster Quarter-Final
Mauricio Pochettino Set To Be Appointed Manchester United Manager
Darragh Murray Named In Irish Squad For Fiji Clash
Portlaoise Panthers Aiming To Bounce Back In Division One
Portarlington On The Road In Leinster
The Down's Building Towards Leinster Football Quarter-Final
Laois Provisional League Fixtures Revealed
The Harps Manager Praises His Sides Efforts In Leinster
Buccaneers Claim Back To Back AIL Wins
Kilcormac Killoughey Captain Full Of Praise For Goalkeeper
Lough Lene Gaels Suffer Late Heartbreak In Leinster Quarter-Final
Crookedwood Win Leinster Junior Camogie Title
Conor Slevin Wins Dramatic Leinster Quarter-Final For Kilcormac Killoughey
Ireland Secure Comfortable Win Over Argentina
Kilcormac Killoughey Seal Win But Heartbreak For Lough Lene Gaels And The Harps