The Los Angeles Chargers have the most games by a team in losses with 350+ passing yards, with 38 games.

nfl team most 350 passing yard games in all-time in losses including playoffs
Interpreted as:
NFL team most 350 or more passing yard games in all-time in losses including playoffs
ChargersSaintsRamsDolphinsCowboysColtsEaglesCardinalsFalconsSteelersBroncosBengalsGiantsPackersBuccaneersRaidersPatriotsWashingtonLionsTitansJetsChiefsVikings3837353231313130292928272727262625252524242322
TEAMGPYDSLCMPATTPCTAVGYDS/GTDTD%INTINT%SCKSCKYRATE
Los Angeles ChargersLos Angeles Chargers3814,675381,0461,73360.48.5386.2784.5704.09769085.8
New Orleans SaintsNew Orleans Saints3714,499371,1611,78765.08.1391.9864.8512.97651994.2
Los Angeles RamsLos Angeles Rams3513,516351,0461,66762.78.1386.2694.1523.111079189.0
Miami DolphinsMiami Dolphins3212,677329461,57959.98.0396.2815.1744.75846683.0
Dallas CowboysDallas Cowboys3112,588319821,54363.68.2406.1734.7624.08964588.1
Indianapolis ColtsIndianapolis Colts3111,809319251,41965.28.3380.9805.6594.25440892.5
Philadelphia EaglesPhiladelphia Eagles3112,028318641,45959.28.2388.0604.1443.09669586.9
Arizona CardinalsArizona Cardinals3011,780308781,39263.18.5392.7644.6453.28960591.8
Atlanta FalconsAtlanta Falcons2911,134299071,37965.88.1383.9695.0372.78157296.0
Pittsburgh SteelersPittsburgh Steelers2911,724298891,40463.38.4404.3684.8473.38155991.8
Denver BroncosDenver Broncos2810,964288221,34960.98.1391.6483.6503.79071283.1
Cincinnati BengalsCincinnati Bengals2710,303277831,24862.78.3381.6655.2433.48160891.8
New York GiantsNew York Giants2710,459277891,25562.98.3387.4574.5393.16246291.4
Green Bay PackersGreen Bay Packers2710,332277621,22862.18.4382.7665.4524.28661389.1
Tampa Bay BuccaneersTampa Bay Buccaneers2610,256267381,18062.58.7394.5605.1524.47040389.0
Oakland RaidersOakland Raiders269,834266921,19158.18.3378.2514.3423.58057184.5
New England PatriotsNew England Patriots259,726257051,14961.48.5389.0585.0403.55235690.8
Washington Football TeamWashington Football Team259,809257131,13462.98.6392.4554.9343.06449894.2
Detroit LionsDetroit Lions259,855257431,21761.18.1394.2574.7363.06348990.0
Tennessee TitansTennessee Titans249,289246811,12560.58.3387.0534.7474.27152485.2
New York JetsNew York Jets249,141246501,11758.28.2380.9474.2514.66754379.7
Kansas City ChiefsKansas City Chiefs239,041236571,03463.58.7393.1575.5313.06148897.3
Minnesota VikingsMinnesota Vikings228,475226701,06762.87.9385.2524.9403.76949188.1
Houston TexansHouston Texans186,7631850782261.78.2375.7425.1242.95335492.6
Chicago BearsChicago Bears186,7361849782060.68.2374.2445.4404.94429984.4
Seattle SeahawksSeattle Seahawks176,4741749576964.48.4380.8395.1192.54934097.4
Cleveland BrownsCleveland Browns176,3781748576563.48.3375.2435.6283.73526293.1
San Francisco 49ersSan Francisco 49ers176,5011747174163.68.8382.4375.0273.63829393.1
Buffalo BillsBuffalo Bills165,9391643474458.38.0371.2334.4405.45634976.3
Jacksonville JaguarsJacksonville Jaguars145,3171438661263.18.7379.8325.2264.24225190.6
Baltimore RavensBaltimore Ravens93,308928346261.37.2367.6153.2122.62214683.0
Carolina PanthersCarolina Panthers72,737720231963.38.6391.0103.1113.42212886.7
StatMuse has team, game-level data for passing yards going back to the 1950 season.