Bamford will miss Tuesday's League Cup tie at Fulham.
Luke Ayling came off with an knee problem at St James' Park, whilst Raphinha was withdrawn with a hip complaint.
Centre-forward Bamford played the full 90 minutes but injured his knee.
Jack Harrison has become the third Leeds player to contract Covid-19 in the last month and Pascal Struijk is one game into a three-match suspension for a much-debated red card against Liverpool. Adam Forshaw and Diego Llorente (both muscular) and Robin Koch (pelvic) also missed Friday's game through injury.
The absentees are testing the Premier League's smallest squad.
Premier League clubs are allowed to register 25 senior players for the start of the season. Leeds have only named 17, although with unlimited under-21 players allowed too, the list does not include first-choice goalkeeper Ilan Meslier.
Nevertheless, 20 men are needed to name a full matchday squad this season.
No other Premier League club has as few senior players registered.
Leeds are clearly relying on quality rather than quantity and showing faith in the ability of their youngsters but apart from Meslier and Ian Poveda, who is on loan at Blackburn Rovers, none of them has made a Premier League start. Only Crysencio Summerville has played in the division at all, appearing for 22 minutes as Raphinha's replacement on Friday.
Amari Miller, Sean McGurk, Lewis Bate, Kristoffer Klaesson and Leo Hjelde were all signed in the summer but only back-up goalkeeper Klaesson made Friday's nine-man bench.
Rodrigo and Tyler Roberts are the two candidates to replace Bamford, with the other likely to be used in midfield. With Bamford so robust, it is a problem that rarely presents itself. The
December 2019 5-4 defeat at Birmingham City is the only league match Bamford has not played any part in over the last three seasons.
Despite mainly being used deeper by Marcelo Bielsa, Rodrigo has often played as Spain's No 9. The Whites used him there at home to West Bromwich Albion last season and in all three cup ties since he has been at the club. The first two were lost - albeit the League Cup tie against Hull City only on penalties - and against Crewe Alexandra in round two, the game only turned Leeds's way when Bamford came off the bench.
Winners of Division Two of Premier League 2 last season, Leeds clearly have talent they believe in beneath the surface. Joe Gelhardt and Sam Greenwood are two highly-regarded strikers signed from Wigan Athletic and Arsenal respectively last summer.
We may soon find out how capable some of those youngsters are of filling the gaps opening up in the senior starting XI.
LEEDS SQUAD: Ayling, Bamford, Cooper, Dallas, Firpo, Forshaw, Harrison, James, Klich, Koch, Llorente, Phillips, Raphinha, Roberts, Rodrigo, Shackleton, Struijk.
Under-21 players (Contract and Scholars): Allen, Andreucci, Bate, Bogusz*, Bradbury, Bray, Brook, Buchan, Caprile*, Carole, Chilokoa-Mullen, Christy, Coleman, Cresswell, Dean, Debayo, Diboe, Drameh, Edmondson*, Ferguson, Galloway, Gelhardt, Godden, Greenwood, Hjelde, Hughes, Jenkins, Kamwa, Kenneh, Klaesson, Littlewood, McCalmont*, McCarron, McGrath, McGurk, McKinstry, Meslier, Mihaylov*, Miller, Moore, Ombang, Picksley, Poveda*, Ragan, Snowdon, Spencer, Summerville, Sutcliffe, Thomas, van den Heuvel.
* out on loan