Ralph Hasenhuttl claims Aston Villa defender Matty Cash handled the ball in the area, calling it a "fantastic save" as Southampton were beaten 1-0.
Ross Barkley scored his first goal since October when he headed home from a Jack Grealish cross to break the deadlock and secure all three points for the visitors.
Southampton had two significant VAR decisions go against them including a 10th-minute penalty shout when Cash blocked Stuart Armstrong's strike.
The ball appeared to strike the hand of the Aston Villa defender and VAR referee Mike Dean took a lengthy look at Cash's outstretched arm, which seemed slightly away from his body, before deciding it was not a penalty.
The official line from VAR was that the ball flicked off the defender's thigh and onto his hand and was not deemed to be a penalty.
"The handball was a good save from the player, it was good goalkeeping I think," Hasenhuttl said.
"It was not the VAR decision, but for us it was definitely a very good save.
"If that's the rule then that's the rule – let's keep on going – but I think it was undeserved to have no point."
In added time, Ings looked to have struck the leveller for Hasenhuttl's men, but the forward was flagged offside. A VAR review ruled the striker's shoulder marginally offside and the on-field decision was upheld, with the manager saying it was fine margins which proved the difference.
🗣 "In such a situation it can be decisive for the game." The boss reacts to a tough night for #SaintsFC: — Southampton FC (@SouthamptonFC) January 30, 2021
The Austrian added: "Exactly. Exactly (it was fine margins) and then this (the fact that it grazed his thigh before hitting his hand) is the reason that it is not a handball and then everybody throws in with everything he has and it is always deflecting.
"Because normally the ball goes up and to the hand but it is a fantastic save because the hand goes towards the ball and he makes a fantastic save.
"But I am normally a big fan of the VAR and I don't want to be too critical today but everyone has to decide if this is OK or not."
Villa went into the game with just one win from their last five games, but scored the decisive goal just before half-time at St Mary's, with manager Dean Smith praising the team performance.
"It was a real tough game against a good team who put us under a lot of pressure but I think the telling moment was the quality of the goal," he said.
"We've had to defend resolutely, we've been on the better side of some marginal decisions tonight for a change which is nice.
"But it was a real resolute team performance where you can't really pick one player out and I thought all of them worked really hard for each other and made it really difficult for them and kept the ball out of the back of the net.
"So a really great result following the game on Wednesday (a 3-2 defeat by Burnley) when we played better than we did today but lost the game."
