The Addicks have been desperately short on firepower all season - mustering a measly 26 goals in their 36 Championship fixtures so far.
Riga, drafted in to help oversee a second tier survival bid, had hoped to address that issue prior to the loan deadline passing.
He was able to bring in midfielder Davide Petrucci from Manchester United and recalled forward Joe Pigott from a stint at Gillingham, but has revealed that he had been hoping for more on the transfer front.
The Belgian said after Saturday's 3-0 defeat away at Derby County: "We were looking, as were a lot of teams, for a striker which we didn't find, so we have to find a solution within our squad.
"Joe Pigott did well and created by himself some chances. It was not easy for him to come into a game we weren't mastering, but he did it well.
"In midfield we don't have a lot of players, we have some wingers. We have Jacko (Johnnie Jackson), Diego (Poyet) and Jordan (Cousins), but we want more options.
"Petrucci is a young player also and played well in difficult circumstances. We need this kind of player, with the number of games we have."
Riga added on Charlton's precarious predicament, which has them perched just above the drop zone: "As I said to the players, we lose a game but the way is still long. Opportunities to do our job are still there.
"It's just a question of recovering the best we can. The most important thing is that we've done it before.
"To have games in hand is an advantage, it can also be a disadvantage. Playing on Tuesday and on Saturday each week - with young players - is even more difficult.
"We knew beforehand the situation so we don't have to complain, we just have to try and do our best, not only on the pitch but outside the pitch, to still have a competitive team."