United midfielder Nemanja Matic had headed a corner across his own goal area and Rodriguez reacted quickly to nod home the victor.
Mourinho said: "We were masters in complicated football, everything was complicated".
They've now won three of the last seven PL titles available.
Increasingly poor conditions and a general lack of thrust continued to inhibit both sides, but United did force Foster into wonderfully save on 66 minutes when he tipped a Lukaku effort around the post.
Manchester United inexplicably lost at home to West Brom, 1-0, in a awful performance.
Sources have told ESPN FC that Martial has become frustrated at a lack of opportunities and will consider his options at the end of the season, amid firm interest from Juventus and Atletico Madrid.
"But the Premier League is one of the nicest and most important".
"We did it in the way we wanted to do", Guardiola said at Wembley on Saturday.
Foster has kept goal for much of this season for West Brom but, ahead of possible keeping a second successive clean sheet at his former stomping ground, the 35-year-old admitted that his main priority was on looking after his family and not, in fact, football.
Afterwards, Mourinho indicated that his players did not execute the game plan as he had hoped.
Following the departure of manager Alan Pardew earlier this month, West Brom sacked technical director Nick Hammond as part of a restructuring plan. But, despite easily being United's most creative player, the midfielder was brought crashing back down when he was hooked with less than an hour played.
Manchester United have kept a league-high 16 clean sheets this season, with 11 of those coming at Old Trafford - also the most in the league.
Mourinho was asked whether he took off Pogba because he had a yellow card and was at risk of getting sent off.
United's comeback at the Etihad from a 2-0 half-time deficit offered their supporters a rare fillip of flair and excitement after a hard season where their style of play has hardly endeared Jose Mourinho to the club's fanbase. According to Adam Marshall, who is a member of United's media team, the forward was unable to join in with the post-match celebrations because he was throwing up in the toilets. "I am pleased we managed to show everyone that". Yet after Manchester United wrenched the trophy out of City's firm grip a week ago having trailed by two goals at half-time, at Old Trafford on Sunday they handed it right back to them.