The Spaniard will line up sixth, next to Lotus rivals Kimi Raikkonen fifth and behind the two Mercedes - who swept the front row with Nico Rosberg on pole - and two Red Bulls.
"I think it's going to be difficult tomorrow," Alonso told reporters. "Nothing is impossible in Formula One, but it's going to be very unlikely that we'll fight for the victory tomorrow."
The double world champion is third overall in the championship, 17 points behind Red Bull's leader Sebastian Vettel, and Monaco's tight and twisty street circuit is a tough place to overtake on.
Alonso can at least hope to bank some solid points, unlike his Brazilian team mate Felipe Massa who will start in last place after crashing heavily in final practice and damaging his car too much for it to be fixed in time for qualifying.
Massa escaped injury, although he said he was experiencing some muscular back pain. He blamed a bump in the road for the incident that pitched the Ferrari into the guardrail on the pit straight and then nose-first into the energy-absorbing plastic barrier at Ste. Devote corner.
"When I braked I touched the bump and maybe the car touched the floor and I locked both front wheels, which is not an easy thing to happen," he told reporters.
"So I hit the guardrail on the left and then it was just waiting for the wall to arrive, which is not a nice feeling."
Despite the prospect of a hard afternoon on Sunday, the Brazilian refused to give up all hope.
"It is the worst track to have this problem but I think we need to be positive," he said. "It is also a track where many things happen during the race. Maybe you have many safety cars. you need to be prepared for the best we can."
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- Motor Racing
- Kimi Raikkonen
- Nico Rosberg
- Sebastian Vettel
- Felipe Massa