He said: "It was a bit frantic early on and I think a few of us were blowing pretty hard. But all credit to the guys, we dug in there well and played some good rugby.
"It was disappointing for Scott that he got sent off but it was important that we stuck to the pattern that we went into the game with after that happened and we did."
Defending Grand Slam winners Wales take on Ireland at Lansdowne Road in the third round of games in the championship on February 26 with everything to play for. Welsh spirits will certainly be high following their victory over Scotland but Peel insisted Wales were not getting carried away after the win having tasted defeat in Dublin two years ago.
He said: "We've come a cropper there a few times in the past but we can go there in a confident mood after the win."