The Jags boss completed his fourth signing of the summer yesterday with the capture of Ben Richards-Everton on a one-year deal, although the former Tamworth kid is now poised to join Airdrie on loan.
Despite also recruiting Ryan Stevenson, Daniel Seabourne and Abdul Osman, the Firhill gaffer remains in the market for more reinforcements.
Archibald said: "I'm hoping to get a few players in and I was keen to get another in for this week but it hasn't happened.
"It's a struggle. We are trying to get good ones but they're hard to come by. It's frustrating.
"We are waiting for them to come to us at times but we won't stop looking as we are very light in numbers at the moment.
"We are looking for a striker and we also need a left-back and a bit of cover elsewhere.
"But we're not worried. We're in a good position because the boys who were here last season have now had a full campaign in the top flight. That stands us in good stead.
"We have a core of players we can rely on but we need more numbers to help them."
After taking four points from their opening two Premiership fixtures against Ross County and Dundee, Partick will host top-flight newcomers Hamilton Accies tomorrow.
It has been an impressive start to the campaign for Alex Neil's side, who have defeated St Mirren and St Johnstone.
Archibald said: "When we met them in the First Division they were one of the hardest teams to play against because they work so hard.
"When Hamilton don't have possession they are one of the most aggressive sides at pressing the ball - and I don't mean that in a kicking sense.
"I don't think that's changed as I've watched a couple of their games recently and they've still shown the same work ethic."
One player who won't be part of the Jags squad tomorrow is Mexican defender Gabriel Piccolo, whose contract was terminated by mutual consent.
SportTimes revealed earlier that he'd been told he was free to find another club after falling out of favour at Firhill.