The Aberdeen midfielder, 24, started in Prague and was withdrawn just before the hour mark as Gordon Strachan's side won their first match of 2016.
"When you get a taste, you always want more," McLean told BBC Scotland.
"I've enjoyed the few days. It's what everybody wants and I hope I can just stay here."
Ikechi Anya's early goal proved to be enough for Scotland in Prague.
"The boys dug in and we got the win, which was great," McLean said.
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"First half was a bit tricky but second half, we were a lot better. We controlled the game in parts.
"It was obviously great to make my debut from the start.
"I felt good for the time I was on the pitch. I didn't feel out of place at all and it's where I want to be."
Strachan selected two squads for the matches against Czech Republic and Denmark, with the latter visiting Hampden on Tuesday.
Hibernian midfielder John McGinn - a former St Mirren team-mate of McLean's - is in the squad to face the Danes and could make his senior international debut in Glasgow.
"Hopefully he can do well enough and stay in," McLean said of 21-year-old McGinn. "You just need to enjoy moments like this - ones you need to cherish."
Alan Hutton, 31, won his 50th Scotland cap in Prague and the Aston Villa full-back described it as "a great honour".
"I never once really thought I'd get this many," he explained. "To get to 50 is a dream come true, really."
Ross McCormack, a late call-up to the squad, set up Anya's goal.
"To get a 1-0 win, we've got to be happy," the 29-year-old Fulham forward said.
"I just had to be strong with the two centre-halves and try and get them out the way.
"To be honest, I didn't see Ikechi, I just heard his shout so I thought if I can get it in that space, with his pace, if it's a foot race he's always going to win. When he got there, he thankfully tucked it in.
"Thankfully, the manager gave me a chance and I enjoyed it."
Kenny McLean is eager to follow up his Scotland debut with more caps after playing in the 1-0 win over Czech Republic.