Ireland had the better of a disappointing game with Boaz Myhill denying Shane Long and debutant Paddy Madden in the second half.
Trapattoni's declared himself happy with his side's performance ahead of their World Cup qualifiers with Sweden and Austria next month.
"Yes, with the performance, we deserved to win. We had three clear chances only for their keeper who was fantastic," Trapattoni told Sky Sports 1.
"We had three or four good opportunities to score, but it's a friendly game and it's pre-season so I am happy.
"I think a draw is enough for us, but I think we deserved to win because we had three or four great opportunities to score.
"Wales are a proud side, even though they were missing (Gareth) Bale and he is
"But it is important we started the season well so we can go on to face Sweden
and Austria in September having achieved a good result and giving ourselves the
confidence to believe we can do well in those games," he added.
Republic of Ireland captain John O'Shea found the positives after the draw.
O'Shea noted: "I am a little bit disappointed. We had a couple of chances to win the game but it wasn't to be.
"I will take the positives and I'll take a clean sheet all day.
"We knew coming here it was going to be the test we wanted."