Cardiff are likely to have more of a defensive examination at Thomond Park against a Munster side that beat Scarlets 34-21 in Llanelli.
“Thomond will be tough but we will back ourselves after a solid start,” said Basham.
“There is plenty to work on personally. I felt a little bit eager at times but wanted to make a good impression and felt I did that.”
Basham started alongside blind-side Alex Mann and number eight Alun Lawrence against Lions, with Dan Thomas replacing him for the closing stages.
Cardiff will be without number eight Taulupe Faletau for a few more weeks after he suffered a calf injury on his return from the summer tour to Japan.
Basham hopes to get a run of games and his focus is club starts rather than adding to his 17 caps.
“It’s an area of tough competition, so my focus is purely on Cardiff. I want to build on from that first game and be the best player I can,” he said.
“I was there for Jac Morgan’s debut against Scotland – it was me, him and Ross Moriart – and Tommy Reffell has been great as well.
“It was tough playing for a side that wasn’t so competitive at times but now I am at a club that is pretty much competitive every game and we are in there going for wins.”