The visitors dominated possession in the cinch Premiership match at Fir Park and Paul McMullan hit the bar but they never seriously tested Liam Kelly despite having 13 shots at goal.
Jason Cummings could not make the most of two good chances and Kelly's only other save was a comfortable one from Lee Ashcroft.
The game was ultimately won by Tony Watt's 34th-minute header after a free-kick from Jake Carroll, who was sent off 12 minutes from time.
When asked about the reports linking him with his former Hibernian team-mate Griffiths, who appears to be well out of favour at Celtic, McPake said: "I've been linked with move for a lot of players.
"The transfer window is getting ready to shut and I'll be linked with a move for maybe three, four, five or six players.
"I'm not going to stand and say what we're looking for but, yes, we're hoping to do business."
McPake, who lost Charlie Adam to a groin injury, added: "We created enough chances. I thought we were very fluent, particularly in the first half, we were causing them all sorts of problems.
"It was a poor goal for us to lose. We did a lot of work on set-plays all week because we felt that's where they could hurt us most.
"But I'm extremely proud of what the players gave out there and on another day you win that game pretty comfortably because, I think everybody will be in agreement with me here, the better team lost that game.
"But it doesn't matter, Motherwell have got the points, fair play to them."
Well boss Graham Alexander felt Carroll's dismissal was harsh after Willie Collum showed a straight red card following a lunge on Max Anderson.
"I thought it was a yellow card at most at the time," he said. "When I watch the millions of slowed-down replays that will be shown, I might change my mind.
"But I thought it was a yellow and if I am wrong then I will say so."
Alexander added: "That was a resilient performance, we weren't at our best so we had to be hard to beat and protect our goal.
"We scored a great goal from a set-piece and it became the deciding factor."
Alexander is closing in on a deal to bring centre-back Sondre Solholm Johansen from Norwegian top-flight side Mjondalen.
"We were working on it when the game was going on," Alexander said.
"I spoke to him a while ago and it has been a drawn-out process but we are delighted to get him in.
"He is a top player who can improve us and hopefully he will be with us on Monday or Tuesday."