The Young Lions earned a straightforward 3-0 triumph over the tournament hosts on Thursday evening, seeing them book their place in the semi-finals for the first time since 2009.
After seeing his men record back-to-back wins, Boothroyd admitted that he is happy with the momentum being built up in Poland.
"It was all doom and gloom after drawing the Sweden game but we have a good group of players and we managed to get the two wins we needed," he told ITV Sport. "It was another high-pressure game, and with Slovakia winning if we hadn't won ours we'd be out.
"The Polish team are big and strong at the back and we felt our best ploy was to use two pacy players in between the lines. And then Tammy Abraham came on and added another dimension.
"We're getting better and better all the time. I think there's more to come from our side. We should be tip-top by Tuesday. We were among the best 12 teams in Europe, and now we're down to the last four. Our next challenge is to get to the last two."
Slovakia beat Sweden 3-0 in the other Group A game on Thursday, leaving them in with a shout of joining England in the semis as the best-placed runners-up.