Such an outcome never materialised, however, as the Irish outfit kept their Heineken Cup hopes alive thanks to tries from George Naoupu and Mata Fifita and 23 points from the boot of Dan Parks. Now Lam has to get hsi team ready to face the fourt-time champions who currently top the Pool after two successive victories.
"We were absolutely gutted we didn't win against Saracens. We knew it was a chance gone,"said Lam, whose team now face four-times continental kings Toulouse in December's double header.
"There were a lot of plaudits for our performance but the question mark was whether we could back it up with our attitude and performance in a game we were expected to win. I was very pleased.
"We had a game plan and the boys carried that out very well. Winning is not a right, you have to go and earn it. We knew that Zebre were targeting this game so to win convincingly was a big effort - we were really clinical."
Lam was particularly impressed by his pack as they showed real steel in the setpiece and created both tries from well-worked lineouts. That was no mean feat against a Zebre pack that included the likes of Marco Bortolami and Mauro Bergamasco, especially when you consider that Connacht have been hit by a host of injury problems this season.
Connacht headed to Parma with the likes of flanker John Muldoon, prop Nathan White and No8 Eoin McKeon on the
sidelines yet they fronted up to provide Parks with the necessary platform to guide them to victory.
"Probably the area I was most pleased about was our forwards. We had so many forwards out but the pack really stepped up and, on the back of that pressure, Dan Parks played extremely well, too," added Lam.
"I have to give a special mention to our forwards coach Dan McFarland, I think he's doing a fantastic job. The two tries we scored were straight off his blackboard. It was the work that he's done, and the boys pulled it off.
"There are so many experienced guys and a lot of a regulars who are missing. It's testament to the culture of the club and the way were are one group. For guys to step in and perform is very pleasing."
The one down side of their first win of the European campaign and their third Heineken Cup success against the Italians in two seasons was another brace of injuries, with James So'oliao and Jason Harris-Wright the unfortunate duo this time around.
Samoan full back So'oliao, who was making his debut, suffered a badly sprained ankle and hooker Harris-Wright had further problems with a recurring bicep injury.