Lallana scored the only goal of the 1-0 win in the 95th minute of the game against the ten-man Slovakians, which was also Allardyce's debut game in charge of the Three Lions.
The manager said: "We were not as clinical as I expected us to be.
"Then Adam scores his first goal for England in the dying seconds. It can never come better than that.
"It puts us on the journey going forward. Hopefully we can get better.
"Slovakia were playing at home but never bothered coming out. It was about breaking that down, but we did it in the end."