The West Brom manager claimed that the Chilean dived during the early stages of the match and should have been booked.
While he also felt a penalty should have been given for the Rodriguez moment, he didn't blame the player for not staying down.
Rodriguez cleverly cut back on Shkodran Mustafi and looked certain to win a penalty when he was up-ended by the Arsenal defender.
MF Granit Xhaka, 6 - Looked off the pace in the first half in particular, and his set-piece delivery was a bit below it's usual high standard.
Lacazette scored the opener when he headed in a rebound after Alexis Sanchez freekick was punched unto his path by Ben Foster.
"West Brom disturbed our build up in the first half but in the second half we controlled the game and did not give anything away".
4th minute: Bundled over by Craig Dawson (goes down easily) to win a free-kick around 25 yards out from the angle.
FW Alexandre Lacazette, 8 - His first goal was the result of his positioning and anticipation, his second a perfectly dispatched penalty.
A brace from Alexandre Lacazette handed the Gunners their third win of the campaign and West Brom their second defeat of the season in the EPL.
"He is easily for me the best technical player at Arsenal", Wright said of the German on BBC Radio 5 Live.
But viewers watching on were nonetheless in shock at referee Bobby Madley's failure to award a spot-kick. The Baggies frontman beat Cech with his header, but Nacho Monreal heroically cleared it off the line.
This was Gareth Barry's 633rd Premier League appearance, which saw him overtake previous record-holder Ryan Giggs in the rankings. "You hope it goes well for them".
BATE have lost just one of their last 12 home games in all European competition (vs Barcelona in October 2015) and are unbeaten in their last seven (W3 D4).
The classic underrated, understated defensive midfielder, his record is likely to stand the rest of time; of current Premier League players, his closest challenger is fellow holding midfielder Michael Carrick, who remains more than 150 games behind.