The Tottenham striker is yet to net in the Premier League this campaign, but slotted away an accomplished chip for England's fifth goal against the European minnows.
And Kane spoke of his delight at finally finding the net, suggesting that the attention around his start to the season was weighing heavily.
"It was great to get on the scoresheet," the 22-year-old told ITV Sport.
"Obviously there's a lot been said about not scoring yet this season. It was a great opportunity for me today.
"When I got off the bench I was looking to get that goal and thankfully I got on the scoresheet.
Kane also illustrated his delight for England captain Wayne Rooney, who equalled Sir Bobby Charlton's Three Lions goalscoring record with a first-half penalty.
"It was great for Wayne to equal the record," Kane added.
"A great achievement so we're all buzzing for him. But the whole team played well.
"We got the job done, first team to qualify and we don't want to stop here. We want to keep improving and continue to push on."