The manager completed his fourth signing of the summer yesterday with the capture of Ben Richards-Everton on a one-year contract, although he is now poised to join Airdrie on loan.
Despite also recruiting Ryan Stevenson, Daniel Seabourne and Abdul Osman, Archibald remains in the market for more reinforcements and 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 host Hamilton tomorrow and Archibald is a big fan of their work ethic. He said: "When we met them in the First Division they were one of the hardest teams to play against because they work so hard."