The economic situation was not at all the same as what drove the Age of Exploration to begin. Europe was bleeding gold and silver to the far east during the Great Bullion famine. Its partly what drove Portugal to explore down the coast of Africa because they knew that there was gold there due to the sub-Saharan trade routes. Even then with state sponsorship and more efficient caravels, just going to sub-Saharan Africa took decades for the Portugese. Spain sought for a shorter route to the spice trade, and then Columbus lied about vast amounts of gold in the New World (and was lucky enough to be right). These gave drive to the Spanish and Portugese to sponsor these sorts of projects, and even early English and French settlements in the New World were focused on finding gold or silver.
There is no such situation in the 11th century. The European powers will still exploring eastern Europe, were still imposing law on 'their' land, and gradually developing. You hadn't yet reached the times when all of Europe was fighting over strips of land along their borders, although they still did that. They were still looking inward in the European theater rather than taking a more global view.
Technology didn't help. Knarrs weren't the best ships for cargo or travel. Better than most of the time, yes, but not quite the equal of caravels or carracks. It could take weeks just to go from Iceland to Greenland, and likely just as long to reach Vinland. So that's like a month and a half or two months from Iceland to the northernmost part of Vinland. Add in a month to reach Iceland from Norway or Germany, and another to reach south of Nova Scotia or start up the St Lawrence River, and its already a major voyage. Knarrs weren't good enough to skip from Newfoundland to Ireland or Norway. The currents also meant they needed to take this northern route. Then you have the fact that exploring new lands is far more difficult than traveling routes you are already aware of. Some estimate that even viking ships could only travel between one and two knots in unfamiliar water, compared to three to six or even more when they knew the currents and reefs. The knarr also wouldn't have sufficient supplies to work for two or three months independently. They'd need to hug the coast while traveling slowly due to unfamiliar currents and underwater landscapes, and also stop occasionally for fresh water and supplies. They'd have no settlements of their own people to stop at to rest and resupply, and they can't talk to the natives. The vikings stopped exploring when it simply wasn't worth it anymore. Hell, I'm pretty sure some of the difficulties of the Vinland settlements was that some of the men were so focused on exploration they outright forgot to properly provision themselves for winter. So it wasn't a lack of will. It simply wasn't realistic with what they had available. They didn't have the supplies to support a significant portion of their men to be exploring rather than working, and they could only explore so far from their settlements in the first place.
So you'd need the sort of explorers that appeared in the Age of Exploration that were financed richly by monarchs to explore and claim lands, and more settlements to resupply and or have the explorers using ships that can carry more supplies and thus can explore further before needing to resupply. Except as noted, the monarchs of this time have different things on their minds. The kings of Norway are more likely to encourage settlement of Vinland through believing it could eventually turn into another Iceland than filling up a map. Norway also didn't have the money to waste on 'frivolous' activities. They'd be spending their resources trying to keep their vassals in line and securing their rule. Really, I'd think the Grand Banks being found and valued enough to secure a few settlements in the region to be more likely than any king deciding to splurge money financing a few ships to explore the coast of a land they'll likely never see. However the Scandinavian countries still had plenty of fishing spots that were more accessible that were still sufficient at the time.