Boaz Myhill twice came to Wales' rescue in the second half with fine saves from Shane Long and Paddy Madden to deny the Republic victory in Cardiff.
Coleman was happy with the test his side faced from the Republic and was happy with the efforts of his players.
"We got a tough game for sure, we knew it would be, they are very well organsied and a big goal threat as we saw tonight Boaz [Myhill] pulled off some terrific saves for us," Coleman told Sky Sports HD1.
"It was a tough match.
"It was good tonight for us to play our style of football (because) we won't come against a tougher team in terms of trying to break them down because they really press you high and make it difficult, but I was happy with guys they worked really hard.
"We rode our luck a couple of times.
"We got a really tough test so I am pleased enough with the team effort."
Coleman has spent most of the week answering questions about Gareth Bale, who watched the game from the stands, but the Welsh boss is happy to deal with the attention having a world class player attracts to Welsh football.
He said: "This week has not really been about Wales and Ireland, to be honest. It's been about is he going or he is staying, is he playing?
"I can't grumble because he's a great player. Only special players get that type of publicity and interest - and he plays for us.
"I'll take the rough with the smooth all day long.
"It'd be nice for the next game if he is fit and settled somewhere. We hope
and pray that happens."