It was not a comfortable 2-1 triumph for the Three Lions, but a pivotal one as they kept alive their hopes of reaching the knockout rounds.
It was a difficult first half for the team as they conceded to Martin Chrien's header, but after the break, England showed glimpses of promise as Alfie Mawson found the equaliser and Nathan Redmond clinched the winner.
"I wasn't [worried] because I work with these lads and know the quality they've got," Boothroyd told talkSPORT. "I think it was about composure over the occasion. Ninety per cent of the stadium was Slovakian, that made it a great atmosphere, but it was certainly partisan and we had to deal with that and be even more composed.
"I thought throughout the game we controlled it, we stopped them and gave them problems, dealt with their big player - [Stanislav] Lobotka - stopped him playing. But when we got on the ball I thought we moved it well, and it was just the final pass, the final cross that we didn't have.
"In the second half we created a lot more chances and freed up the front two players who I thought were excellent, and we gave ourselves a chance of winning it, and thankfully we did."
England's final Group A game will be against Poland.