Posh won the game 3-0, but needed in-form loan goalkeeper Lucas Bergstrom to make a couple of big saves including one from Morecambe’s Cole Stockton at 1-0 early in the first-half.
Morecambe have one point from their opening two matches and have yet to score a goal.
But Adams said: “We caused Peterborough problems. They scored a goal against the run of play to take the lead, a shot from outside of the area that found its way into the back of the net, and that was unexpected.
“We all know how good Peterborough are, but players such as [Ash] Hunter, [Jensen] Weir and [Jake] Taylor were causing them problems, which is promising going forward.
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“We are two games into the season and we have picked up one point, but we’ve played against two very good teams and there is a long way to go.
“We have to take the chances when they come along, we haven't today, but that is just the nature of football.”