"The priority is to get another striker in," Rodgers told BBC Sport Wales.
"Gorka is now injured with his shoulder for a few months so we really need that support."
Beattie, 26, endured an injury-hit first season at the Liberty Stadium since joining for a club-record £500,000 a year ago.
The Scotland international had hoped to make a fresh start as new campaign got underway.
But he picked up a calf injury in pre-season and did not feature in the 2-0 opening day defeat at Hull last weekend or Tuesday's 3-0 Carling Cup win over Barnet in midweek.
Allen eager for Liberty boost
He is still a couple of weeks away from a return while Spaniard Pintado's injury is more long-term.
It is a blow for Rodgers who is trying to rid the Swans of the Championship's lowest scorers tag which they picked up last season for scoring just 40 goals in 46 games.
But his immediate concern is securing a first league win at home to Preston North End on Saturday.
"It probably wasn't the ideal start last week at Hull but obviously we got a good win during the week in the cup," added Rodgers.
"That always breeds confidence, no matter how it comes. There's teams that have lost their first two games and that can always leave a wee sense of anticipation for that win.
"But we got a good win and performed well during the week and now we take that confidence into Saturday's game and am looking for another good performance."
Source: BBC Sport
Source: BBC Sport