The Leeds United head coach believes Phillips' injury isn't serious and the Whites didn't make a call on their enforcer's availability for the Yorkshire derby until yesterday.
Phillips appeared on the pitch at full-time to salute the Elland Road crowd, who made up the highest home attendance of the season and celebrated a return to the Championship top spot.
"Until yesterday he had a lot of possibilities to play," said Bielsa of Phillips and the injury.
"Yesterday finally we decided for him not to play. It is not serious. The last match he had a limit but he tolerated the pain well.
"He felt more uncomfortable [after] but we hope to have him back next week."
Goals from Luke Ayling and Patrick Bamford, a wonderstrike and a tap-in respectively, gave the Whites a seven-point gap to the play-off spots.
Bielsa was content with his team's overall performance, having stifled the Terriers' creativity and made other chances for themselves - Jack Harrison hitting the woodwork for the second game running.
"It was a match where we defended well," said Bielsa.
"We didn't concede real chances, just the one in the first half. And offensively we could have scored maybe one more goal. But anyway the team did very well in attack as well."
The Argentine was pleased to see Bamford hit the net, for the first time in eight games and hopes the moment will be a catalyst for more goals in the Championship run-in.
"I'm happy for him," said Bielsa.
"Centre forwards need to score. He couldn't do it for a long time.
"Today he scored a typical centre forward goal. I hope it is going to be useful for him to score more times."
Leeds were again missing the injured Jean-Kevin Augustin [hamstring] and there was no place in the squad once again for Ian Poveda, even with Jordan Stevens missing out through illness. Bielsa felt he had options for every position in the substitutes bench he named.
"Stevens was sick all week," said Bielsa.
"We consider Oliver Casey as a possible midfielder, not a centre-back, and for us Pascal [Struijk] is a centre back, necessary to be in the group of 18 players. Pascal, [Barry] Douglas are defenders, Olly and [Jamie] Shackleton midfielders, [Gjanni] Alioski and [Tyler] Roberts attackers."