McInnes felt the Dons were "pushed about" too easily in Perth as their title dream all but ended with their defensive frailties exposed.
"We got dominated at both ends of the pitch and the more determined team won," McInnes told BBC Scotland.
"I know what I need to get in but there won't be wholesale changes."
With Ash Taylor injured, McInnes handed a debut to 20-year-old defender Michael Rose, but he went off injured at half-time with Aberdeen 2-0 down following a David Wotherspoon free-kick and Steven MacLean adding a second.
More defensive mistakes followed as Liam Craig took advantage of a Mark Reynolds error to make it three.
"We were lacking in physicality, we were vulnerable at every set play," said McInnes, whose side remain eight points behind Premiership leaders Celtic.
"We didn't win enough headers. When we don't have Ash Taylor in the team - he gives us real size and aggression at centre-back - we never had that dominance there.
"There's been a few games this season where we've lacked that physicality, strength and size. We need to make sure we get more players in the building in the summer that can deal with that and stand up to that.
"The introduction of [Barry] Robson, a guy at 37 and a young boy at 16, Connor McLennan, making his debut - they played the game with the enthusiasm and determination that everyone should have treated the game.
"When the game is a technical game we can take on anybody. But tonight we needed more strength of character, we needed more first headers, we needed physicality because we got pushed about tonight and the best team won."
St Johnstone manager Tommy Wright saw his side move into fourth in the Premiership and was delighted with their dominant performance.
"Tonight we made it so difficult for them from the first whistle in terms of the pressure we put them under and how hard we worked," said Wright.
"That gave us a platform to go and play well; lots of good possession, lots of good balls into the box. It was a really good performance and when we're like that we're a match for anybody.
"I thought [Graham] Cummins was good tonight, that is him back to his best. MacLean gives us what he gives us all the time and young Joe Shaughnessy at the back I thought was strong.
"Overall I thought everybody played extremely well."

Owen Lane's two tries set Wales on their way with Reuben Morgan-Williams and Phil Jones also crossing for the hosts.
Robbie Smith, Blair Kinghorn and Ben Appleson were Scotland's try scorers.
Wales begin their World Rugby Junior Championship campaign in Georgia against Australia on 31 May,
They will also face England and Samoa in Pool A, while Scotland are in Pool B with Ireland, New Zealand and Italy.
Aberdeen manager Derek McInnes will attempt to sign more physical players this summer after they were swept aside 3-0 by St Johnstone at McDiarmid Park.
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Wales Under-20s warmed up for the 2017 World Rugby Junior Championship with a 29-22 victory over Scotland at Bridgend's Brewery Field.